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

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

Published online by Cambridge University Press:  15 June 2016

E. I. Khukhro ,
N. Yu. Makarenko  and
P. Shumyatsky
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

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.

Keywords

finite groupLie ringderived lengthFitting heightnilpotency classautomorphism

MSC classification

Secondary: 20D45: Automorphisms 17B40: Automorphisms, derivations, other operators 20F40: Associated Lie structures 20F50: Periodic groups; locally finite groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 2 , May 2017 , pp. 391 - 412
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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