On a generalization of one Kramer's theorem

TL;DR

This paper investigates a conjecture related to supersoluble groups, demonstrating its falsity in general but confirming its validity for groups with a trivial Frattini subgroup.

Contribution

It disproves a 2012 conjecture on supersoluble groups and establishes its validity for a specific class of groups.

Findings

The conjecture is false in the general case.

The conjecture holds for groups with trivial Frattini subgroup.

Abstract

Yangming Li and Xianhua Li in 2012 proposed a conjecture that generalizes O.U. Kramer's result about supersoluble groups. Here we proved that this conjecture is false in the general case and true for groups with the trivial Frattini subgroup.