Khukhro, E. I. and Makarenko, N. Yu. and Shumyatsky, P.
(2017)
*Finite groups and Lie rings with an automorphism of order 2n.*
Proceedings of the Edinburgh Mathematical Society, 60
(2).
pp. 319-412.
ISSN 0013-0915

Item Type: | Article |
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Item Status: | Live Archive |
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## Abstract

Abstract. Suppose that a finite group G admits an automorphism ϕ of order 2n such that the fixed-point subgroup CG (ϕ2n−1) of the involution ϕ2n−1 is nilpotent of class c. Let m = |CG (ϕ)| be the number of fixed points of ϕ. 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.

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