On a Finite Group Generated by Subnormal Supersoluble Subgroups

TL;DR

This paper proves that a finite group generated by two subnormal supersoluble subgroups with a nilpotent derived subgroup is itself supersoluble, expanding understanding of group structure under these conditions.

Contribution

It establishes the supersolubility of a finite group generated by subnormal supersoluble subgroups with a nilpotent derived subgroup, under specific subgroup conditions.

Findings

Finite group generated by subnormal supersoluble subgroups with nilpotent derived subgroup is supersoluble

Conditions for supersolubility in generated groups are clarified

Enhances understanding of subgroup influence on overall group structure

Abstract

Supersolubility of a finite group $G=\langle A,B\rangle$ with the nilpotent derived subgroup $G^\prime$ is established under the condition that the subgroups $A$ and $B$ are both subnormal and supersoluble.