Exponent of a finite group with a fixed-point-free four-group of automorphisms
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Let e be a positive integer and G a finite group acted on by the four-group V in such a manner that C G (V) = 1. Suppose that V contains an element v such that the centralizer C G (v) has exponent e. Then the exponent of G″, the second derived group of G, is bounded in terms of e only.
KeywordsFinite Group Normal Closure Nilpotency Class Invariant Subgroup Involutory Automorphism
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