Locally finite groups containing a $$2$$ 2 -element with Chernikov centralizer

Khukhro, E. I.; Makarenko, N. Yu.; Shumyatsky, Pavel

doi:10.1007/s00605-014-0701-8

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2016

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“…In our recent paper [17] we also used Theorem 1.1 to prove that if a locally finite group G has a 2-element g with Chernikov centralizer such that the involution in g has nilpotent centralizer, then G has a soluble subgroup of finite index.…”

Section: Introductionmentioning

confidence: 99%

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

Khukhro

Makarenko

Shumyatsky

2016

Proceedings of the Edinburgh Mathematical Society

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Suppose that a finite group G admits an automorphism ϕ of order 2 n such that the fixed-point subgroup C G (ϕ 2 n−1 ) of the involution ϕ 2 n−1 is nilpotent of class c. Let m = |C G (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.1991 Mathematics Subject Classification. Primary 20D45; secondary 17B40, 20F40, 20F50.

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Section: Introductionmentioning

confidence: 99%