2022/06/30 by A. Ballester‐Bolinches, S. Y. Madanha, Ballester-Bolinches, A. +5
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2206.15466
openalex publication_date 2022/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A classical result of Baer states that a finite group G which is the product of two normal supersoluble subgroups is supersoluble if and only if G' is nilpotent. In this article we show that if G=AB is the product of supersoluble (respectively, w -supersoluble) subgroups A and B , A is normal in G , B permutes with every maximal subgroup of each Sylow subgroup of A , then G is supersoluble (respectively, w -supersoluble) provided that G' is nilpotent. We also investigate products of subgroups defined above when A∩ B=1 and obtain more general results.