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Some generalizations of Shao and Beltrán’s theorem

Minghui Li

School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, Guangxi, P. R. China

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Jiakuan Lu

School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, Guangxi, P. R. China

E-mail Address: jklu@gxnu.edu.cn

Corresponding author.

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Boru Zhang

School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, Guangxi, P. R. China

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, and

Wei Meng

School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, Guangxi, P. R. China

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https://doi.org/10.1142/S0219498823500676Cited by:1 (Source: Crossref)

Abstract

Let G and A be finite groups of relative coprime orders and A act on G via automorphisms. In this paper, we prove that when every maximal A-invariant subgroup of G that contains the normalizer of some Sylow subgroup has prime index, then G is supersolvable; if every non-nilpotent maximal A-invariant subgroup of G has prime index or is normal in G, then G is a Sylow tower group.

Communicated by R. Camina

Keywords:

AMSC: 20D10, 20D20

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