Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-19T02:17:09.300Z Has data issue: false hasContentIssue false
  • English
  • Français

Stable decompositions of classifying spaces of finite abelian p-groups

Published online by Cambridge University Press:  24 October 2008

John C. Harris  and
Nicholas J. Kuhn
John C. Harris
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA, U.S.A.
Nicholas J. Kuhn
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, VA, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

Let BG be the classifying space of a finite group G. Consider the problem of finding a stable decomposition

into indecomposable wedge summands. Such a decomposition naturally splits E*(BG), where E* is any cohomology theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 3 , May 1988 , pp. 427 - 449
Copyright
Copyright © Cambridge Philosophical Society 1988

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

REFERENCES

[1]Adams, J. F.. Infinite Loop Spaces. Annals of Math. Study no. 90 (Princeton University Press, 1978).CrossRefGoogle Scholar
[2]Adams, J. F., Gunawakdena, J. H. and Miller, H. R.. The Segal conjecture for elementary abelian p-groups. Topology 24 (1985), 435–460.CrossRefGoogle Scholar
[3]Carlisle, D.. Ph.D. thesis, University of Manchester (1985).Google Scholar
[4]Carlisle, D., private correspondence.Google Scholar
[5]Carlisle, D. and Kuhn, N. J.. Subalgebras of the Steenrod algebra and the action of matrices on truncated polynomial algebras. J. Algebra, to appear.Google Scholar
[6]Carlisle, D. and Kuhn, N. J.. Some smash product decompositions (in preparation).Google Scholar
[7]Carlsson, G.. Equivariant stable homotopy and Segal's Burnside ring conjecture. Ann. of Math. (2) 120 (1984), 189–224.CrossRefGoogle Scholar
[8]Clifford, A. H. and Preston, G. B.. Algebraic Theory of Semigroups, Vol. 1. Math. Surveys of the A.M.S. no. 7, (1961).CrossRefGoogle Scholar
[9]Curtis, C. W. and Reiner, I.. Methods of Representation Theory vol. I, (Wiley, 1981).Google Scholar
[10]Glover, D. J.. A study of certain modular representations. J. Algebra 51 (1978), 425–475.Google Scholar
[11]Harris, J. C.. Ph.D. thesis, University of Chicago (1985).Google Scholar
[12]Howie, J. M.. An Introduction to Semigroup Theory (Academic Press, 1976).Google Scholar
[13]Humphreys, J. E.. Ordinary and modular characters of SL (3, p). J. Algebra, 72 (1981), 8–16.CrossRefGoogle Scholar
[14]Huppert, B.. Endliche Gruppen I (Springer-Verlag, 1967).Google Scholar
[15]James, G. and Kerber, A.. The Representation Theory of the Symmetric Group. Encyclopedia of Math., vol. 16 (Addison-Wesley, 1981).Google Scholar
[16]Kuhn, N. J.. Suspension spectra and homology equivalences. Trans. Amer. Math. Soc. 283 (1984), 303–313.Google Scholar
[17]Kuhn, N. J.. The Morava K-theory of some classifying spaces. Trans Amer. Math. Soc. 304 (1987), 193–205.Google Scholar
[18]Kuhn, N. J.. The rigidity of L(n). In Algebraic Topology – Proceedings, Seattle 1985, Lecture Notes in Math. vol. 1286 (Springer-Verlag 1987), pp. 286–292.Google Scholar
[19]Lallemont, G. and Petrich, M.. Irreducible matrix representations of finite semigroups. Trans Amer. Math. Soc. 139 (1969), 392–412.Google Scholar
[20]Landrock, P.. Finite Group Algebras and their Modules. London Math. Soc. Lecture Note Series no. 84 (Cambridge University Press, 1983).Google Scholar
[21]Lannes, J. and Schwartz, L.. On the structure of the -injectives. Preprint.Google Scholar
[22]May, J. P.. Stable maps between classifying spaces. Amer. Math. Soc. Cont. Math. 37 (1985), 121–129.Google Scholar
[23]Mitchell, S. A. and Priddy, S. B.. Symmetric product spectra and splittings of classifying spaces. Amer. J. Math. 106 (1984), 219–232.Google Scholar
[24]Mitchell, S. A. and Priddy, S. B.. Stable splittings derived from the Steinberg module. Topology 22 (1983), 285–298.Google Scholar
[25]Mitchell, S. A.. Splitting B(ℤ/p)n and BT n via modular representation theory. Math. Z. 189 (1985), 1–9.Google Scholar
[26]Nishida, G.. Stable homotopy type of classifying spaces of finite groups. Preprint (1985).Google Scholar
[27]Rotman, J. J., The Theory of Groups (Allyn and Bacon, 1973).Google Scholar
[28]Serre, J. P.. Linear Representation of Finite Groups. Graduate Texts in Math. vol. 42 (Springer-Verlag, 1977).Google Scholar
[29]Steinberg, R.. Lectures on Chevalley Groups. Yale Lecture Notes (1967).Google Scholar
[30]Swan, R.. The p-period of a finite group. Illinois J. Math. 4 (1960), 341–346.Google Scholar
[31]Schwartz, L.. (In preparation.)Google Scholar
[32]Toda, H.. p-primary components of homotopy groups IV. Mem. Coll. See. Kyoto, Series A 32 (1959), 297–332.Google Scholar