Coprime actions with supersolvable fixed-point groups

Author:

Meng Hangyang1,Guo Xiuyun1

Affiliation:

1. Department of Mathematics , Shanghai University , Shanghai 200444 , P. R. China

Abstract

Abstract Let A be an elementary abelian r-group acting on a finite r {r^{\prime}} -group G. Suppose that the fixed-point group C G ( a ) {\operatorname{C}_{G}(a)} is supersolvable for each a A # {a\in A^{\#}} . We show that G is supersolvable if | A | r 4 {|A|\geqslant r^{4}} and that G 𝐅 3 ( G ) {G^{\prime}\leqslant\mathbf{F}_{3}(G)} if | A | r 3 {|A|\geqslant r^{3}} . Moreover, we prove some other results for cases when the fixed-point group C G ( a ) {\operatorname{C}_{G}(a)} is abelian, p-nilpotent or satisfies the Sylow tower property.

Funder

National Natural Science Foundation of China

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

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1. Coprime actions with p-nilpotent centralizers;Journal of Algebra;2020-09

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