Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-06-03T12:15:18.684Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  07 September 2011

Michael Aschbacher
Affiliation:
California Institute of Technology
Radha Kessar
Affiliation:
University of Aberdeen
Bob Oliver
Affiliation:
Université de Paris XIII
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[Ad] J. F., Adams, Stable Homotopy and Generalized Homology, Univ. Chicago Press (1974).Google Scholar
[Al1] J., Alperin, Sylow intersections and fusion, J. Algebra, 6 (1967), 222–241.Google Scholar
[Al2] J., Alperin, Local Representation Theory, The Santa Cruz conference on finite groups, Proc. Symp. Pure Math., 37, Amer. Math. Soc., Providence (1980), 369–375.Google Scholar
[Al3] J. L., Alperin, Weights for finite groups, The Arcata Conference on Finite Groups, Proc. Sympos. Pure Math., 47, Amer. Math. Soc., Providence (1987), 369–379.Google Scholar
[ABG] J., Alperin, R., Brauer, and D., Gorenstein, Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups, Trans. Amer. Math. Soc., 151 (1970), 1–261.Google Scholar
[AB] J. L., Alperin and M., Broué, Local methods in block theory, Ann. of Math., 110 (1979), 143–157.Google Scholar
[ABC] T., Altinel, A., Borovik, & G., Cherlin, Simple groups of finite Morley rank, Math. Surveys & Monogr., 145, American Math. Soc. (2008).Google Scholar
[AOV] K., Andersen, B., Oliver, & J., Ventura, Reduced, tame, and exotic fusion systems, preprint.
[A1] M., Aschbacher, A characterization of Chevalley groups over fields of odd order, Annals of Math., 106 (1975), 353-468.Google Scholar
[A2] M., Aschbacher, On finite groups of component type, Illinois J. Math., 19 (1975), 87-113.Google Scholar
[A3] M., Aschbacher, On finite groups of Lie type and odd characteristic, J. Algebra, 66 (1980), 400-424.Google Scholar
[A4] M., Aschbacher, Finite Group Theory, Cambridge Univ. Press (1986).Google Scholar
[A5] M., Aschbacher, Normal subsystems of fusion systems, Proc. London Math. Soc., 97 (2008), 239–271.Google Scholar
[A6] M., Aschbacher, The generalized Fitting subsystem of a fusion system, Memoirs Amer. Math. Soc., 209 (2011), nr. 986.Google Scholar
[A7] M., Aschbacher, Generation of fusion systems of characteristic 2-type, Invent. Math., 180 (2010), 225–299.Google Scholar
[A8] M., Aschbacher, S3-free 2-fusion systems, Proc. Edinburgh Math. Soc., (proceedings of the 2009 Skye conference on algebraic topology, group theory and representation theory, to appear).
[A9] M., Aschbacher, N-groups and fusion systems, preprint.
[AC] M., Aschbacher & A., Chermak, A group-theoretic approach to a family of 2-local finite groups constructed by Levi and Oliver, Annals of Math., 171 (2010), 881–978.Google Scholar
[ASm] M., Aschbacher and S., Smith, The Classification of the Quasithin Groups, American Mat. Soc., (2004).
[Ben]H., Bender, Finite groups with dihedral Sylow 2-subgroups, J. Algebra, 70 (1981), 216–228.Google Scholar
[BG] H., Bender and G., Glauberman, Characters of finite groups with dihedral Sylow 2-subgroups, J. Algebra, 70 (1981), 200–215.Google Scholar
[Be1] D., Benson, Representations and Cohomology I: Cohomology of Groups and Modules,Cambridge Univ. Press (1991).Google Scholar
[Be2] D., Benson, Representations and Cohomology II: Cohomology of Groups and Modules, Cambridge Univ. Press (1991).Google Scholar
[Be3] D., Benson, Cohomology of sporadic groups, finite loop spaces, and the Dickson invariants, Geometry and cohomology in group theory, London Math. Soc. Lecture notes ser. 252, Cambridge Univ. Press (1998). 10–23.Google Scholar
[Bo]R., Boltje, Alperin's weight conjecture in terms of linear source modules and trivial source modules, Modular representation theory of finite groups (Charlottesville, VA, 1998), de Gruyter, Berlin (2001), 147–155.Google Scholar
[BonD] V.M., Bondarenko, J.A., Drozd, The representation type of finite groupsZap. anchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov, 57 (1977) 24-41. English translation: J. Soviet Math., 20(1982), 2515–2528.Google Scholar
[Bf] P., Bousfield, On the p-adic completions of nonnilpotent spaces, Trans. Amer. Math. Soc., 331 (1992), 335–359.Google Scholar
[BK] P., Bousfield & D., Kan, Homotopy limits, completions, and localizations, Lecture notes in math., 304, Springer-Verlag (1972).Google Scholar
[Br1] R., Brauer, Investigations on group characters, Ann. of Math., (2) 42 (1941), 936–958.Google Scholar
[Br2] R., Brauer, Some applications of the theory of blocks of characters of finite groups IV, J. Algebra,17 (1971), 489–521.Google Scholar
[Br3] R., Brauer, On 2-blocks with dihedral defect groups, Symposia Mathematica, Vol. XIII (Convegno di Gruppi e loro Rappresentazioni, INDAM, Rome, 1972), Academic Press, London (1974), 367–393.Google Scholar
[Br4] R., Brauer, On the structure of blocks of characters of finite groups, Proc. Second Intern. Conf. on Theory of Groups, Lecture Notes in Mathematics 372, Springer-Verlag, (1974).Google Scholar
[Bre] S., Brenner, Modular representations of p-groupsJ. Algebra, 15 (1970), 89-102.Google Scholar
[5a1] C., Broto, N., Castellana, J., Grodal, R., Levi, & B., Oliver, Subgroup families controlling p-local finite groups, Proc. London Math. Soc., 91 (2005), 325–354.Google Scholar
[5a2] C., Broto, N., Castellana, J., Grodal, R., Levi, & B., Oliver, Extensions of p-local finite groups, Trans. Amer. Math. Soc., 359 (2007), 3791-3858.Google Scholar
[BL] C., Broto & R., Levi, On spaces of self homotopy equivalences of p-completed classifying spaces of finite groups and homotopy group extensions, Topology, 41 (2002), 229–255.Google Scholar
[BLO1] C., Broto, R., Levi, & B., Oliver, Homotopy equivalences of p-completed classifying spaces of finite groups, Invent. Math., 151 (2003), 611–664.Google Scholar
[BLO2] C., Broto, R., Levi, & B., Oliver, The homotopy theory of fusion systems, J. Amer. Math. Soc., 16 (2003), 779–856.Google Scholar
[BLO3] C., Broto, R., Levi, & B., Oliver, Discrete models for the p-local homotopy theory of compact Lie groups and p-compact groups, Geometry and Topology, 11 (2007), 315-427.Google Scholar
[BLO4] C., Broto, R., Levi, & B., Oliver, A geometric construction of saturated fusion systems, An alpine anthology of homotopy theory (proceedings Arolla 2004), Contemp. math. 399 (2006), 11-39.Google Scholar
[BLO] C., Broto, R., Levi, & B., Oliver, The theory of p-local groups: A survey, Homotopy theory (Northwestern Univ. 2002), Contemp. math., 346, Amer. Math. Soc. (2004), 51–84.
[BM] C., Broto & J., Møller, Chevalley p-local finite groups, Algebr. & Geom. Topology, 7 (2007), 1809–1919.Google Scholar
[BMO] C., Broto, J., Møller, & B., Oliver, Equivalences between fusion systems of finite groups of Lie type, preprint.
[B2] M., Broué, Isométries parfaites, types de blocs, catégories dérivées, Astérisque, 181-182 (1990) 61–92.Google Scholar
[BP1] M., Broué and L., Puig, A Frobenius theorem for blocks, Invent. Math., 56 (1980), no.2, 117–128.Google Scholar
[BP2] M., Broué and L., Puig, Characters and Local structures in G-Algebras, Journal of Algebra, 63, (1980), 51–59.Google Scholar
[Br] K., Brown, Cohomology of Groups, Springer-Verlag (1982).Google Scholar
[Bu] W., Burnside, The Theory of Groups of Finite Order, Cambridge Univ. Press (1897).Google Scholar
[Cm] N., Campbell, Pushing Up in Finite Groups, Thesis, Cal. Tech., (1979).
[Ca] G., Carlsson, Equivariant stable homotopy and Sullivan's conjecture, Invent. Math., 103 (1991), 497–525.Google Scholar
[CE] H., Cartan & S., Eilenberg, Homological Algebra, Princeton Univ. Press (1956).Google Scholar
[CL] N., Castellana & A., Libman, Wreath products and representations of p-local finite groups, Advances in Math., 221 (2009), 1302–1344.Google Scholar
[COS] A., Chermak, B., Oliver, & S., Shpectorov, The linking systems of the Solomon 2-local finite groups are simply connected, Proc. London Math. Soc., 97 (2008), 209–238.Google Scholar
[CP] M., Clelland & C., Parker, Two families of exotic fusion systems, J. Algebra, 323 (2010), 287–304.Google Scholar
[CPW]G., Cliff, W., Plesken, A., Weiss, Order-theoretic properties of the center of a block, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), Proc. Sympos. Pure Math., 47, Part 1, Amer. Math. Soc., Providence, RI (1987), 413–420.Google Scholar
[Cr1] D., Craven, Control of fusion and solubility in fusion systems, J. Algebra, 323 (2010), 2429–2448.Google Scholar
[Cr2] D., Craven, The Theory of Fusion Systems: an Algebraic Approach, Cambridge Univ. Press (2011).Google Scholar
[Cr3] D., Craven, Normal subsystems of fusion systems, Journal London Math. Soc. (to appear).
[CG] D., Craven & A., Glesser, Fusion systems on small p-groups, Trans. Amer. Math. Soc. (to appear).
[CrEKL] D., Craven, C., Eaton, R., Kessar, M., Linckelmann, The structure of blocks with a Klein 4 defect group, Math. Z. (to appear).
[Cu] E., Curtis, Simplicial homotopy theory, Adv. in Math., 6 (1971), 107–209.Google Scholar
[CuR1] C. W., Curtis and I., Reiner. Representation theory of finite groups and associative algebras, Wiley-Interscience (1962).Google Scholar
[CuR2] C. W., Curtis and I., Reiner. Methods in representation theory, Vol. I, J. Wiley and Sons (1981).Google Scholar
[CuR3] C. W., Curtis and I., Reiner. Methods in representation theory, Vol. II, J. Wiley and Sons (1987).Google Scholar
[Da1] E.C., Dade, Blocks with cyclic defect groups, Ann. of Math., 84 (1966), 20–48.Google Scholar
[Da2] E.C., Dade, Counting characters in blocks I, Invent. Math., 109 (1992), no. 1, 187–210.Google Scholar
[Da3] E.C., Dade, Counting characters in blocks II, J. Reine Angew. Math., 448 (1994), 97–190.Google Scholar
[Da4] E.C., Dade, Counting characters in blocks, II.9, in Representation Theory of Finite Groups, Ohio State University Math Research Institute Publications, Vol. 6, de Gruyter, Berlin (1997), 45–59.Google Scholar
[DGMP1] A., Díaz, A., Glesser, N., Mazza, & S., Park, Control of transfer and weak closure in fusion systems, J. Algebra, 323 (2010), 382–392.Google Scholar
[DGMP2] A., Díaz, A., Glesser, N., Mazza, & S., Park, Glauberman's and Thompson's theorems for fusion systems, Proc. Amer. Math. Soc., 137 (2009), 495–503.Google Scholar
[DGPS] A., Díaz, A., Glesser, S., Park, & R., Stancu, Tate's and Yoshida's theorem for fusion systems, Journal London Math. Soc. (to appear).
[DN1] A., Díaz & A., Libman, Segal's conjecture and the Burnside ring of fusion systems, J. London Math. Soc., 80 (2009), 665–679.Google Scholar
[DN2] A., Díaz & A., Libman, The Burnside ring of fusion systems, Adv. Math., 222 (2009), 1943–1963.Google Scholar
[DRV] A., Díaz, A., Ruiz & A., Viruel, All p-local finite groups of rank two for odd prime p, Trans. Amer. Math. Soc., 359 (2007), 1725–1764.Google Scholar
[Dr] A., Dress, Induction and structure theorems for orthogonal representations of finite groups, Annals of Math., 102 (1975), 291–325.Google Scholar
[Dw] W., Dwyer, Homology decompositions for classifying spaces of finite groups, Topology, 36 (1997), 783–804.Google Scholar
[DK1] W., Dwyer & D., Kan, Realizing diagrams in the homotopy category by means of diagrams of simplicial sets, Proc. Amer. Math. Soc., 91 (1984), 456–460.Google Scholar
[DK2] W., Dwyer & D., Kan, Centric maps and realizations of diagrams in the homotopy category, Proc. Amer. Math. Soc., 114 (1992), 575–584.Google Scholar
[Er] K., Erdmann, Blocks of tame representation type and related algebras, Lecture Notes in Mathematics, 1428, Springer-Verlag, Berlin (1990).Google Scholar
[Fe] W., Feit, The Representation Theory of Finite Groups, North Holland (1982).Google Scholar
[FT] W., Feit and J., Thompson, Solvability of groups of odd order, Pacific J. Math., 13 (1963), 775–1029; 218–270; 354–393.Google Scholar
[FF] R., Flores and R., Foote, Strongly closed subgroups of finite groups, Adv. in Math., 222 (2009), 453-484.Google Scholar
[F] R., Foote, A characterization of finite groups containing a strongly closed 2-subgroup, Comm. Alg., 25 (1997), 593–606.Google Scholar
[Fr] E., Friedlander, Étale Homotopy of Simplicial Schemes, Annals of Mathematics Studies, vol. 104, Princeton University Press (1982).Google Scholar
[Gl1] G., Glauberman, Central elements in core-free groups, J. Algebra, 4 (1966), 403–420.Google Scholar
[Gl2] G., Glauberman, Factorizations in local subgroups of finite groups, Regional Conference Series in Mathematics, 33, Amer. Math. Soc. (1977).Google Scholar
[GN] G., Glauberman & R., Niles, A pair of characteristic subgroups for pushing-up in finite groups, Proc. London Math. Soc., 46 (1983), 411–453.Google Scholar
[GZ] P., Gabriel & M., Zisman, Calculus of Fractions and Homotopy Theory, Springer-Verlag (1967).Google Scholar
[GJ] P., Goerss & R., Jardine, Simplicial Homotopy Theory, Birkhäauser Verlag (1999).Google Scholar
[Gd1] D., Goldschmidt, A conjugation family for finite groups, J. Algebra, 16 (1970), 138–142.Google Scholar
[Gd2] D., Goldschmidt, Strongly closed 2-subgroups of finite groups, Annals of Math., 102 (1975), 475–489.Google Scholar
[Gd3] D., Goldschmidt, 2-fusion in finite groups, Annals of Math., 99 (1974), 70-117.Google Scholar
[G1] D., Gorenstein, Finite groups, Harper & Row (1968).Google Scholar
[G2] D., Gorenstein, The Classification of the Finite Simple Groups, I, Plenum (1983).Google Scholar
[GH] D., Gorenstein and M., Harris, Finite groups with product fusion, Annals of Math., 101 (1975), 45–87.Google Scholar
[GL] D., Gorenstein and R., Lyons, Nonsolvable finite groups with solvable 2-local subgroups, J. Algebra, 38 (1976), 453–522.Google Scholar
[GLS3] D., Gorenstein, R., Lyons, and R., Solomon, The Classification of the Finite Simple Groups, Number 3, Mathematical Surveys and Monographs, vol. 40, Amer. Math. Soc. (1998).Google Scholar
[GLS6] D., Gorenstein, R., Lyons, and R., Solomon, The Classification of the Finite Simple Groups, Number 6, Mathematical Surveys and Monographs, vol. 40, Amer. Math. Soc. (2005).Google Scholar
[GW1] D., Gorenstein and J., Walter, The characterization of finite simple groups with dihedral Sylow 2-subgroups, J. Algebra, 2 (1964), 85–151; 218–270; 354–393.Google Scholar
[GW2] D., Gorenstein and J., Walter, Balance and generation in finite groups, J. Algebra, 33 (1975), 224-287.Google Scholar
[GHL] D., Green, L., Héthelyi, & M., Lilienthal, On Oliver's p-group conjecture, Algebra Number Theory, 2 (2008), 969–977.Google Scholar
[GHM] D., Green, L., Héthelyi, & N., Mazza, On Oliver's p-group conjecture: II, Math. Annalen, 347 (2010), 111–122.Google Scholar
[Gr] J., Grodal, Higher limits via subgroup complexes, Annals of Math., 155 (2002), 405–457.Google Scholar
[Ht] A., Hatcher, Algebraic Topology, Cambridge Univ. Press (2002).Google Scholar
[H] D., Higman, Indecomposable representations at characteristic p, Duke J. Math., 21 (1954), 377–381.Google Scholar
[HV] J., Hollender & R., Vogt, Modules of topological spaces, applications to homotopy limits and E∞ structures, Arch. Math., 59 (1992), 115–129.Google Scholar
[IsNa] I.M., Isaacs and G., Navarro, New refinements of the McKay conjecture for arbitrary finite groups, Annals of Math., 156 (2002), 333–344.Google Scholar
[JM] S., Jackowski & J., McClure, Homotopy decomposition of classifying spaces via elementary abelian subgroups, Topology, 31 (1992), 113–132.Google Scholar
[JMO] S., Jackowski, J., McClure, & B., Oliver, Homotopy classification of self-maps of BG via G-actions, Annals of Math., 135 (1992), 183–270.Google Scholar
[JS] S., Jackowski & J., Stomińska, G-functors, G-posets and homotopy decompositions of G-spaces, Fundamenta Math., 169 (2001), 249–287.Google Scholar
[J] Z., Janko, Nonsolvable finite groups all of whose 2-local subgroups are solvable,I, J. Algebra, 21 (1972), 458–517.Google Scholar
[K1] R., Kessar, Introduction to block theory, Group Representation Theory, EPFL Press, Lausanne (2007) 47–77.Google Scholar
[Ke1] R., Kessar, The Solomon system FSol(3) does not occur as fusion system of a 2-blockJ. Algebra, 296, no. 2 (2006), 409–425.Google Scholar
[KL] R., Kessar & M., Linckelmann, ZJ-theorems for fusion systems, Trans. Amer. Math. Soc., 360 (2008), 3093–3106.Google Scholar
[KS] R., Kessar, R., Stancu, A reduction theorem for fusion systems of blocks, J. Algebra, 319 (2008), 806–823.Google Scholar
[KKoL] R., Kessar, S., Koshitani, M., Linckelmann, Conjectures of Alperin and Broué for 2-blocks with elementary abelian defect groups of order 8, J. Reine Angew. Math. (to appear).
[KKuM] R., Kessar, N., Kunugi, N., Mitsuhashi, On saturated fusion systems and Brauer indecomposability of Scott modules, J. Algebra (to appear).
[KR] R., Knörr and G. R., Robinson, Some remarks on a conjecture of Alperin, J. London Math. Soc. (2), 39 (1989), no. 1, 48–60.Google Scholar
[KoZ] S., Koenig, A., Zimmermann, Derived equivalences for group rings, Lecture Notes in Mathematics, 1685, Springer-Verlag, Berlin (1998).Google Scholar
[Ku] B., Küshammer, Lectures on block theory, London Mathematical Society Lecture Note Series 161, Cambridge Univ. Press, Cambridge (1991).Google Scholar
[KulP] B., Külshammer, L., Puig, Extensions of nilpotent blocks, Invent. Math., 102, no. 1 (1990), 17–71.Google Scholar
[KulOW] B., Külshammer, A., Watanabe, and T., Okuyama, A lifting theorem with applications to blocks and source algebras, J. Algebra, 232, no. 1 (2000), 299–309.Google Scholar
[La] J., Lannes, Sur les espaces fonctionnels dont la source est le classifiant d'un p-groupe abélien élémentaire, Publ. Math. I.H.E.S., 75 (1992), 135–244.Google Scholar
[LS] I., Leary & R., Stancu, Realising fusion systems, Algebra & Number Theory, 1 (2007), 17–34.Google Scholar
[LO] R., Levi & B., Oliver, Construction of 2-local finite groups of a type studied by Solomon and Benson, Geometry & Topology, 6 (2002), 917–990.Google Scholar
[LO2] R., Levi & B., Oliver, Correction to: Construction of 2-local finite groups of a type studied by Solomon and Benson, Geometry & Topology, 9 (2005), 2395–2415.Google Scholar
[LR] R., Levi & K., Ragnarsson, p-local finite group cohomology, Homotopy, Homology, Appl. (to appear).
[Lb] A., Libman, The normaliser decomposition for p-local finite groups, Alg. Geom. Topology, 6 (2006), 1267–1288.Google Scholar
[LbS] A., Libman & N., Seeliger, Homology decompositions and groups inducing fusion systems, preprint.
[LV] A., Libman & A., Viruel, On the homotopy type of the non-completed classifying space of a p-local finite group, Forum Math., 21 (2009), 723–757.Google Scholar
[Li1] M., Linckelmann, The isomorphism problem for cyclic blocks and their source algebras. Invent. Math., 125 (1996), 265-283.Google Scholar
[Li2] M., Linckelmann, Fusion category algebras, J. Algebra, 277, no. 1 (2004), 222–235.Google Scholar
[Li3] M., Linckelmann, Simple fusion systems and the Solomon 2-local groups, J. Algebra, 296, no. 2 (2006), 385–401.Google Scholar
[Li4] M., Linckelmann, Alperin's weight conjecture in terms of equivariant Bredon cohomology, Math. Z., 250, no. 3 (2005), 495–513.Google Scholar
[Li5] M., Linckelmann, Trivial source bimodule rings for blocks and p-permutation equivalences, Trans. Amer. Math. Soc., 361 (2009), 1279–1316.Google Scholar
[Li6] M., Linckelmann, On H*(C:kx) for fusion systems, Homology, Homotopy Appl., 11, no. 1 (2009), 203–218.Google Scholar
[LP] J., Lynd & S., Park, Analogues of Goldschmidt's thesis for fusion systems, J. Algebra, 324 (2010), 3487–3493.Google Scholar
[McL] S., MacLane, Homology, Springer-Verlag (1975).Google Scholar
[MP1] J., Martino & S., Priddy, Stable homotopy classification of BGp. Topology, 34 (1995), 633–649.Google Scholar
[MP2] J., Martino & S., Priddy, Unstable homotopy classification of BGp, Math. Proc. Cambridge Phil. Soc., 119 (1996), 119–137.Google Scholar
[May] J.P., May, Simplicial Objects in Algebraic Topology, Univ. Chicago Press (1967).Google Scholar
[MSS] U., Meierfrankenfeld, B., Stellmacher, and G., Stroth, Finite groups of local characteristic p: an overview, Groups, Combinatorics, and Geometry (Durham 2001), World Sci. Publ. (2003), 155–192.Google Scholar
[Mi] H., Miller, The Sullivan conjecture on maps from classifying spaces, Annals of Math., 120 (1984), 39–87.Google Scholar
[Ms] G., Mislin, On group homomorphisms inducing mod-p cohomology isomorphisms, Comment. Math. Helv., 65 (1990), 454–461.Google Scholar
[NT] H., Nagao and Y., Tsushima, Representations of Finite Groups, Academic Press, Boston (1988).Google Scholar
[OW] T., Okuyama and M., Wajima, Irreducible characters of p-solvable groupsProc. Japan Acad. Ser. A Math. Sci., 55 (1979), no. 8, 309–312.Google Scholar
[O1] B., Oliver, Higher limits via Steinberg representations, Comm. in Algebra, 22 (1994), 1381–1402.Google Scholar
[O2] B., Oliver, Equivalences of classifying spaces completed at odd primes, Math. Proc. Camb. Phil. Soc., 137 (2004), 321–347.Google Scholar
[O3] B., Oliver, Equivalences of classifying spaces completed at the prime two, Memoirs Amer. Math. Soc., 848 (2006).Google Scholar
[O4] B., Oliver, Extensions of linking systems and fusion systems, Trans. Amer. Math.Soc., 362 (2010), 5483–5500.Google Scholar
[O5] B., Oliver, Splitting fusion systems over 2-groups, Proc. Edinburgh Math. Soc., proceedings of the 2009 Skye conference on algebraic topology, group theory and representation theory (to appear).
[OV1] B., Oliver & J., Ventura, Extensions of linking systems with p-group kernel, Math. Annalen, 338 (2007), 983-1043.Google Scholar
[OV2] B., Oliver & J., Ventura, Saturated fusion systems over 2-groups, Trans. Amer. Math. Soc., 361 (2009), 6661–6728.Google Scholar
[Ols] J. B., Olsson, On 2-blocks with quaternion and quasidihedral defect groupsJ. Algebra, 36 (1975), 212-241.Google Scholar
[Ols2] J. B., Olsson, On subpairs and modular representation theory, J. Algebra, 76 (1982), 261–279.Google Scholar
[OS] S., Onofrei and R., Stancu, A characteristic subgroup for fusion systems, J. Algebra, 322 (2009), 1705–1718.Google Scholar
[Pa1] S., Park, The gluing problem for some block fusion systems, J. Algebra, 323 (2010), 1690–1697.Google Scholar
[Pa2] S., Park, Realizing a fusion system by a single finite group, Arch. Math., 94 (2010), 405-410.Google Scholar
[P1] L., Puig, Structure locale dans les groupes finis, Bull. Soc. Math. France Suppl. Mém., 47 (1976).Google Scholar
[P2] L., Puig, Local fusions in block source algebras, J. Algebra, 104, no. 2 (1986), 358–369.Google Scholar
[P3] L., Puig, Nilpotent blocks and their source algebras, Invent. Math., 93, no. 1 (1988), 77–116.Google Scholar
[P4] L., Puig, The Nakayama conjecture and the Brauer pairsSeminaire sur les groupes finis III, Publications Matehmatiques De L'Université Paris VII, 171–189.
[P5] L., Puig, The hyperfocal subalgebra of a block, Invent. math., 141 (2000), 365–397.Google Scholar
[P6] L., Puig, Frobenius categories, J. Algebra, 303 (2006), 309–357.Google Scholar
[P7] L., Puig, Frobenius Categories versus Brauer Blocks, Birkhäser (2009).Google Scholar
[PUs] L., Puig and Y., Usami, Perfect isometries for blocks with abelian defect groups and cyclic inertial quotients of order 4, J. Algebra, 172 (1995), 205–213.Google Scholar
[Rg] K., Ragnarsson, Classifying spectra of saturated fusion systems, Algebr. Geom. Topol., 6 (2006), 195–252.Google Scholar
[RSt] K., Ragnarsson & R., Stancu, Saturated fusion systems as idempotents in the double Burnside ring, preprint.
[Ri1] J., Rickard, Derived categories and stable equivalence, J. Pure Appl. Algebra, 61, no. 3 (1989), 303–317.Google Scholar
[Ri2] J., Rickard, Splendid equivalences: derived categories and permutation modules, Proc. London Math. Soc. (3), 72, no. 2 (1996), 331–358.Google Scholar
[RS] K., Roberts & S., Shpectorov, On the definition of saturated fusion systems, J. Group Theory, 12 (2009), 679–687.Google Scholar
[Ro1] G. R., Robinson, Local structure, vertices and Alperin's conjecture, Proc. London Math. Soc., 72 (1996), 312–330.Google Scholar
[Ro2] G. R., Robinson, Weight conjectures for ordinary characters, J. Algebra, 276 (2004), 761–775.Google Scholar
[Ro3] G., Robinson, Amalgams, blocks, weights, fusion systems, and finite simple groups, J. Algebra, 314 (2007), 912–923.Google Scholar
[Rz] A., Ruiz, Exotic normal fusion subsystems of general linear groups, J. London Math. Soc., 76 (2007), 181–196.Google Scholar
[RV] A., Ruiz & A., Viruel, The classification of p-local finite groups over the extraspecial group of order p3 and exponent p, Math. Z., 248 (2004), 45–65.Google Scholar
[Sa1] B., Sambale, 2-blocks with mimimal non-abelian defect groups, J. Algebra (to appear).
[Sa2] B., Sambale, Blocks with defect group, J. Pure Appl. Algebra (to appear).
[Sa3] B., Sambale, Fusion systems on metacyclic 2-groups, preprint.
[Sg] G., Segal, Classifying spaces and spectral sequences, Publ. Math. I.H.E.S., 34 (1968), 105–112.Google Scholar
[Se1] J. P., Serre, Corps Locaux, Hermann (1968).Google Scholar
[Se2] J.-P., Serre, Trees, Springer-Verlag (1980).Google Scholar
[Sm] F., Smith, Finite simple groups all of whose 2-local subgroups are solvable, J. Algebra, 34 (1975), 481–520.Google Scholar
[So] R., Solomon, Finite groups with Sylow 2-subgroups of type .3, J. Algebra, 28 (1974), 182–198.Google Scholar
[Sta1] R., Stancu, Control of fusion in fusion systems, J. Algebra Appl., 5 (2006), 817–837.Google Scholar
[Sta2] R., Stancu, Equivalent definitions of fusion systems, preprint.
[Stn] R., Steinberg, Lectures on Chevalley Groups, Yale Lecture Notes (1967).Google Scholar
[St1] B., Stellmacher, A characteristic subgroup of S4-free groups, Israel J. Math., 94 (1996), 367–379.Google Scholar
[St2] B., Stellmacher, An application of the amalgam method: the 2-local structure of N-groups of characteristic 2-type, J. Algebra, 190 (1997), 11–67.Google Scholar
[Sw] R., Switzer, Algebraic Topology, Springer-Verlag (1975).Google Scholar
[Th] J., Thévenaz, G-Algebras and Modular Representation Theory, Oxford Science Publications (1995).Google Scholar
[Th1] J., Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, I, Bull. Amer. Math. Soc., 74 (1968), 383–437; II, Pacific J. Math., 33 (1970), 451–536; III, Pacific J. Math., 39 (1971), 483–534; IV, Pacific J. Math., 48(1973), 511–592; V, Pacific J. Math., 50 (1974), 215–297; VI, Pacific J. Math., 51 (1974), 573–630.Google Scholar
[Th2] J., Thompson, Simple 3′-groups, Symposia Math., 13 (1974), 517–530.Google Scholar
[Tu] A., Turull, Strengthening the McKay Conjecture to include local fields and local Schur indices, J. Algebra, 319 (2008), 4853–4868.Google Scholar
[Un] K., Uno, Conjectures on character degrees for the simple Thompson group, Osaka J. Math., 41 (2004), 11–36.Google Scholar
[W] J., Walter, The B-Conjecture; characterization of Chevalley groups, Memoirs Amer. Math. Soc., 61 no. 345 (1986), 1–196.Google Scholar
[Wb1] P., Webb, A split exact sequence of Mackey functors, Comment. Math. Helv., 66 (1991), 34–69.Google Scholar
[Wb2] P.J., Webb, Standard stratifications of EI categories and Alperin's weight conjecture, J. Algebra, 320 (2008), 4073–4091.Google Scholar
[Wei] C., Weibel, An Introduction to Homological Algebra, Cambridge Univ. Press (1994).Google Scholar
[Wh] G., Whitehead, Elements of Homotopy Theory, Springer-Verlag (1978).Google Scholar
[Wo] Z., Wojtkowiak, On maps from holim F to Z (Algebraic topology, Barcelona, 1986), Lecture notes in math., 1298, Springer-Verlag (1987), –227–236.Google Scholar
[Zi] K., Ziemiański, Homotopy representations of SO(7) and Spin(7) at the prime 2, Jour. Pure Appl. Algebra, 212 (2008), 1525–1541.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Michael Aschbacher, California Institute of Technology, Radha Kessar, University of Aberdeen, Bob Oliver, Université de Paris XIII
  • Book: Fusion Systems in Algebra and Topology
  • Online publication: 07 September 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9781139003841.007
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Michael Aschbacher, California Institute of Technology, Radha Kessar, University of Aberdeen, Bob Oliver, Université de Paris XIII
  • Book: Fusion Systems in Algebra and Topology
  • Online publication: 07 September 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9781139003841.007
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Michael Aschbacher, California Institute of Technology, Radha Kessar, University of Aberdeen, Bob Oliver, Université de Paris XIII
  • Book: Fusion Systems in Algebra and Topology
  • Online publication: 07 September 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9781139003841.007
Available formats
×