On finite groups in which some maximal invariant subgroups have indices a prime or the square of a prime

2025/01/03 by Jiangtao Shi, Shi, Jiangtao, Yunfeng Tian +1
Mathematics · #20D10 #20D20 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2501.01735

openalex publication_date 2025/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A and G be finite groups such that A acts coprimely on G by automorphisms, we first prove some results on the solvability of finite groups in which some maximal A-invariant subgroups have indices a prime or the square of a prime. Our results generalize Hall's theorem and some other known results. Moreover, we obtain a complete characterization of finite groups in which every non-nilpotent maximal A-invariant subgroup that contains the normalizer of some A-invariant Sylow subgroup has index a prime.

Related

• Finite groups in which some particular non-nilpotent maximal invariant subgroups have indices a prime-power
• Extensions of a theorem of P. Hall on indexes of maximal subgroups
• Finite groups with some particular maximal invariant subgroups being nilpotent or all non-nilpotent maximal invariant subgroups being normal
• Finite groups in which every maximal invariant subgroup of order divisible by p is nilpotent
• Indices of non-supersolvable maximal subgroups in finite groups