MATHEMATICS

On some groups from the formation of supersoluble finite groups

T. I. Vasilyeva

Belarusian State University of Transport, Gomel

Abstract: In this work, for a maximal subgroup of a group $G$, the concept of an $n$-modularly embedded subgroup ($n$ is some natural number) is introduced. A criterion is established under which every maximal subgroup in $G$ is $n$-modularly embedded, as well as necessary and sufficient conditions under which in every subgroup $A$ of $G$ any maximal subgroup is $n$-modularly embedded in $A$ for some natural number $n$, $n\leqslant k$ ($k$ — fixed natural number).

Keywords: supersoluble group, maximal subgroup, $n$-modularly embedded subgroup, Schunck class.

UDC: 512.542

Received: 04.04.2024

Language: English

DOI: 10.54341/20778708_2024_2_59_64