On finite groups in which every non-nilpotent maximal invariant subgroup is normal-Reference-Cited by-同舟云学术

On finite groups in which every non-nilpotent maximal invariant subgroup is normal

Published:2024-01-12 Issue: Volume: Page:
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Shi Jiangtao¹^ORCID,Liu Yifan¹^ORCID

Affiliation:

1. School of Mathematics and Information Sciences, Yantai University, Yantai 264005, P. R. China

Abstract

Let [Formula: see text] and [Formula: see text] be finite groups such that [Formula: see text] acts coprimely on [Formula: see text] by automorphisms, we prove that if every non-nilpotent maximal [Formula: see text]-invariant subgroup of [Formula: see text] is normal, then [Formula: see text] is [Formula: see text]-nilpotent or [Formula: see text]-closed for each prime divisor [Formula: see text] of [Formula: see text], which improves a theorem obtained by Beltán and Shao.

Funder

NSFC

Shandong Provincial Natural Science Foundation, China

Graduate Innovation Foundation of Yantai University

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498825501658

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