This article is cited in 2 papers

Finite groups with given systems of propermutable subgroups

A. A. Trofimuk

Department of Physics and Mathematics, Brest State A.S. Pushkin University, 21 Kosmonavtov Boulevard, 224016, Brest, Belarus

Abstract: Let $H$ be a subgroup of a finite group $G$. Then we say that $H$ is propermutable in $G$ provided $G$ has a subgroup $B$ such that $G = NG(H)B$ and $H$ permutes with all subgroups of $B$. In this paper, we present new properties of propermutable subgroups. Also we provide new information on the structure of a group with propermutable Sylow (Hall, maximal) subgroups and a group $G = AB$ with propermutable subgroups $A$ and $B$.

Keywords and phrases: supersoluble group, propermutable subgroup, saturated formation, factorized groups, Sylow and maximal subgroups.

MSC: 20D10, 20D40

Received: 19.02.2023

Language: English

DOI: 10.32523/2077-9879-2024-15-1-91-97