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Class preserving automorphisms of finite p-groups: a survey

Published online by Cambridge University Press:  05 July 2011

Manoj K. Yadav
Affiliation:
Harish-Chandra Research Institute
C. M. Campbell
Affiliation:
University of St Andrews, Scotland
M. R. Quick
Affiliation:
University of St Andrews, Scotland
E. F. Robertson
Affiliation:
University of St Andrews, Scotland
C. M. Roney-Dougal
Affiliation:
University of St Andrews, Scotland
G. C. Smith
Affiliation:
University of Bath
G. Traustason
Affiliation:
University of Bath
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Publisher: Cambridge University Press
Print publication year: 2011

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References

[1] J. E., Adney and T., Yen, Automorphisms of a p-group, Illinois J. Math. 9 (1965), 137–143.Google Scholar
[2] W., Burnside, Theory of groups of finite order, 2nd Ed., Dover Publications, Inc., 1955. Reprint of the 2nd edition (Cambridge, 1911).Google Scholar
[3] W., Burnside, On the outer automorphisms of a group, Proc. London Math. Soc. (2) 11 (1913), 40–42.Google Scholar
[4] E. C., Dade and M. K., Yadav, Finite groups with many product conjugacy classes, Israel J. Math. 154 (2006), 29–49.Google Scholar
[5] R., Dark and C. M., Scoppola, On Camina groups of prime power order, J. Algebra 181 (1996), 787–802.Google Scholar
[6] W., Feit and G. M., Seitz, On finite rational groups and related topics, Illinois J. Math. 33 (1988), 103–131.Google Scholar
[7] M., Fuma and Y., Ninomiya, “Hasse principle” for finite p-groups with cyclic subgroups of index p2, Math. J. Okayama Univ. 46 (2004), 31–38.Google Scholar
[8] P., Hall, The classification of prime power groups, Journal für die reine und angewandte Mathematik 182 (1940), 130–141.Google Scholar
[9] H., Heineken, Nilpotente Gruppen, deren sämtliche Normalteiler charakteristisch sind, Arch. Math. (Basel) 33 (1980), no. 6, 497–503.Google Scholar
[10] A., Herman and Y., Li, Class preserving automorphisms of Blackburn groups, J. Austral. Math. Soc. 80 (2006), 351–358.Google Scholar
[11] M., Hertweck, Class-preserving automorphisms of finite groups, J. Algebra 241 (2001), 1–26.Google Scholar
[12] M., Hertweck, Contributions to the integral representation theory of groups, Habilitationsschrift, University of Stuttgart (2004). Available at http://elib.uni-stuttgart.de/opus/volltexte/2004/1638
[13] M., Hertweck and E., Jespers, Class-preserving automorphisms and normalizer property for Blackburn groups, J. Group Theory 12 (2009), 157–169.Google Scholar
[14] W., Gaschütz, Nichtabelsche p-gruppen besitzen äussere p-automorphismen, J. Algebra 4 (1966), 1–2.Google Scholar
[15] R., James, The groups of order p6 (p an odd prime), Math. Comp. 34 (1980), 613–637.Google Scholar
[16] M., Kumar and L. R., Vermani, “Hasse principle” for extraspecial p-groups, Proc. Japan Acad. 76, Ser. A, no. 8 (2000), 123–125.Google Scholar
[17] M., Kumar and L. R., Vermani, “Hasse principle” for groups of order p4, Proc. Japan Acad. 77, Ser. A, no. 6 (2001), 95–98.Google Scholar
[18] M., Kumar and L. R., Vermani, On automorphisms of some p-groups, Proc. Japan Acad. 78, Ser. A, no. 4 (2002), 46–50.Google Scholar
[19] I., Malinowska, On quasi-inner automorphisms of a finite p-group, Publ. Math. Debrecen 41 (1992), no. 1–2, 73–77.Google Scholar
[20] I., Malinowska, p-automorphisms of finite p-groups: problems and questions, Advances in Group Theory (1992), 111–127.Google Scholar
[21] T., Ono, A note on Shafarevich–Tate sets for finite groups, Proc. Japan Acad. 74, Ser. A (1998), 77–79.Google Scholar
[22] T., Ono, On Shafarevich-Tate sets, Advanced Studies in Pure Mathematics: Class Field Theory — Its Centenary and prospect 30 (2001), 537–547.Google Scholar
[23] T., Ono and H., Wada, “Hasse principle” for free groups, Proc. Japan Acad. 75, Ser. A (1999), 1–2.Google Scholar
[24] T., Ono and H., Wada, “Hasse principle” for symmetric and alternating groups, Proc. Japan Acad. 75, Ser. A (1999), 61–62.Google Scholar
[25] C. H., Sah, Automorphisms of finite groups, J. Algebra 10 (1968), 47–68.Google Scholar
[26] M., Suzuki, Group Theory II, Springer, New York — Berlin — Heidelberg — Tokyo (1986).Google Scholar
[27] F., Szechtman, n-inner automorphisms of finite groups, Proc. Amer. Math. Soc. 131 (2003), 3657–3664.Google Scholar
[28] H., Wada, “Hasse principle” for SLn(D), Proc. Japan Acad. 75, Ser. A (1999), 67–69.Google Scholar
[29] H., Wada, “Hasse principle” for GLn (D), Proc. Japan Acad. 76, Ser. A (2000), 44–46.Google Scholar
[30] G. E., Wall, Finite groups with class preserving outer automorphisms, J. London Math. Soc. 22 (1947), 315–320.Google Scholar
[31] M. K., Yadav, Class preserving automorphisms of finite p-groups, J. London Math. Soc. 75 (2007), no. 3, 755–772.Google Scholar
[32] M. K., Yadav, On automorphisms of finite p-groups, J. Group Theory 10 (2007), 859–866.Google Scholar
[33] M. K., Yadav, On automorphisms of some finite p-groups, Proc. Indian Acad. Sci. (Math. Sci.) 118 (2008), no. 1, 1–11.Google Scholar

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