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Finite Groups and Lie Rings with an Automorphism of Order 2n
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 60 / Issue 2 / May 2017
- Published online by Cambridge University Press:
- 15 June 2016, pp. 391-412
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- Article
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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.
of order 2
of the involution 
is nilpotent of class 
) be the number of fixed points of 