Finite Groups and Lie Rings with an Automorphism of Order 2n

E. I. Khukhro; N. Yu. Makarenko; P. Shumyatsky

doi:10.1017/S0013091516000225

Finite Groups and Lie Rings with an Automorphism of Order 2n

Part of: Lie algebras and Lie superalgebras Special aspects of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press: 15 June 2016

E. I. Khukhro ,

N. Yu. Makarenko and

P. Shumyatsky

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E. I. Khukhro: Affiliation:
Sobolev Institute of Mathematics, Novosibirsk, 630 090, Russia (khukhro@yahoo.co.uk; natalia_makarenko@yahoo.fr) University of Lincoln, Brayford Pool, Lincoln LN6 7TS, UK
N. Yu. Makarenko: Affiliation:
Sobolev Institute of Mathematics, Novosibirsk, 630 090, Russia (khukhro@yahoo.co.uk; natalia_makarenko@yahoo.fr)
P. Shumyatsky: Affiliation:
Department of Mathematics, University of Brasilia, DF 70910-900, Brazil (pavel@unb.br)

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Abstract

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Abstract

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Suppose that a finite group G admits an automorphism of order 2n such that the fixed-point subgroup of the involution is nilpotent of class c. Let m = ) be the number of fixed points of . It is proved that G has a characteristic soluble subgroup of derived length bounded in terms of n, c whose index is bounded in terms of m, n, c. A similar result is also proved for Lie rings.