On an extension of Shlyk's theorem

2025/06/03 by Shi, Jiangtao, Xu, Fanjie, Li, Na
#20D10 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2506.02885

Abstract

In this paper, we prove that the intersection of all non-nilpotent maximal subgroups of a non-solvable group containing the normalizer of some Sylow subgroup is nilpotent, which provides an extension of Shlyk's theorem.

Citations

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

Related

• 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 subgroup is nilpotent or normal or has p'-order
• Sylow subgroups for distinct primes and intersection of nilpotent subgroups
• On Maximal Subgroups of a Finite Solvable Group
• p-sylowizers and p-nilpotency of finite groups