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A GENERALIZED FIXED-POINT-FREE ACTION
https://doi.org/10.1142/S0219498812501721Cited by:0 (Source: Crossref)
Abstract
In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x ∈ CG(A) of prime order or of order 4, every conjugate of x in G is also contained in CG(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.
