On the structure of groups, possessing Carter subgroups of odd order

TL;DR

This paper proves that in finite groups with a Carter subgroup of odd order, all composition factors are either abelian or isomorphic to a specific simple group, providing insight into the group's structure.

Contribution

It establishes a classification of composition factors in finite groups with Carter subgroups of odd order, identifying specific possible simple groups.

Findings

All composition factors are either abelian or isomorphic to L_2(3^{2n+1})

Provides structural constraints on finite groups with Carter subgroups of odd order

Enhances understanding of the composition structure in such groups

Abstract

In the note we prove that all composition factors of a finite group possessing a Carter subgroup of odd order either are abelain, or are isomorphic to $L_2(3^{2n+1})$.