Finite groups with some particular maximal invariant subgroups being nilpotent or all non-nilpotent maximal invariant subgroups being normal

2024/08/02 by Shi, Jiangtao, Xu, Fanjie · 1 citation
#20D10 #20D25 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2408.01249

Abstract

Let A and G be finite groups such that A acts coprimely on G by automorphisms. We provide a complete classification of a finite group G in which every maximal A-invariant subgroup containing the normalizer of some A-invariant Sylow subgroup is nilpotent. Moreover, we show that both the hypothesis that every maximal A-invariant subgroup of G containing the normalizer of some A-invariant Sylow subgroup is nilpotent and the hypothesis that every non-nilpotent maximal A-invariant subgroup of G is normal are equivalent.

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