Finite groups with some weakly HC− embedded and supersolvable supplemented subgroups

2025/12/22 by M. Ramadan, Mohamed Ramadan
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Algebraic structures and combinatorial models

paper · doi:10.1080/00927872.2025.2596311

Abstract

Let G be a finite group. A subgroup H of G is called weakly HC− embedded in G if there exists a normal subgroup T of G such that HG=HT and Hg∩NT(H)≤H for all g∈G, where HG is the normal closuer of H in G. A subgroup H of G has a supersolvable supplement in G if there exists a supersolvable subgroup K of G such that G=HK. In this paper, we investigate the structure of G under the assumption that certain subgroups of G of prime power orders either are weakly HC− embedded in G or have supersolvable supplements in G. Our results improved and generalized some recent results in the literature.

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