p-Nilpotent maximal subgroups in finite groups

2024/02/28 by Antonio Beltrán, Beltrán, Antonio, Changguo Shao +1
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2402.18413

openalex publication_date 2024/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime number and suppose that every maximal subgroup of a finite group is either p-nilpotent or has prime index. Such group need not be p-solvable, and we study its structure by proving that only one nonabelian simple group of order divisible by p, which belongs to the family \rm PSL_n(q), can be involved in it. For p=2, we specify more, and in fact, such simple group must be isomorphic to \rm PSL₂(r^a) for certain values of the prime r and the parameter a.

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• Finite groups in which some particular non-nilpotent maximal invariant subgroups have indices a prime-power
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