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A fixed-point theorem for central elements in quasisimple groups

Author: Harvey I. Blau
Journal: Proc. Amer. Math. Soc. 122 (1994), 79-84
MSC: Primary 20D05; Secondary 20C25
MathSciNet review: 1254833
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Abstract: It is shown that with a few exceptions (which are listed), any central element in a quasisimple finite group fixes some conjugacy class of the group under multiplication.

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  • [ABEF] Z. Arad, H. I. Blau, J. Erez, and E. Fisman, Real table algebras and applications to finite groups of extended Camina-Frobenius type, J. Algebra (to appear). MR 1292783 (95h:16025)
  • [CCNPW] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of finite groups, Clarendon Press, Oxford, 1985. MR 827219 (88g:20025)
  • [FS] W. Feit and G. M. Seitz, On finite rational matrix groups and related topics, Illinois J. Math. 33 (1988), 103-131. MR 974014 (90a:20016)
  • [I] I. M. Isaacs, Character theory of finite groups, Academic Press, New York, 1976. MR 0460423 (57:417)
  • [G] D. Gorenstein, Finite simple groups: An introduction to their classification, Plenum Press, New York, 1982. MR 698782 (84j:20002)
  • [S1] I. Schur, Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 139 (1911), 155-250.
  • [S2] -, Gesammelte Abhandlungen, Springer-Verlag, Berlin and New York, 1973.
  • [SS] T. A. Springer and R. Steinberg, Conjugacy classes, Seminar on Algebraic Groups and Related Finite Groups, Lecture Notes in Math., vol. 131, Springer-Verlag, Berlin and New York, 1970. MR 0268192 (42:3091)
  • [T] R. C. Thompson, Commutators in the special and general linear groups, Trans. Amer. Math. Soc. 101 (1961), 16-33. MR 0130917 (24:A771)

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Keywords: Quasisimple group, simple group, Schur multiplier, conjugacy class
Article copyright: © Copyright 1994 American Mathematical Society

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