Indices of non-supersolvable maximal subgroups in finite groups

TL;DR

This paper characterizes the structure of non-solvable finite groups where all maximal subgroups are either supersolvable or have prime or squared prime index, extending classic solvability results.

Contribution

It provides a detailed description of non-solvable finite groups with specific maximal subgroup index conditions, building on foundational theorems.

Findings

Characterization of non-solvable groups with specified maximal subgroup indices

Extension of classic solvability theorems to broader group classes

Structural insights into groups with supersolvable or prime-squared prime index maximal subgroups

Abstract

Two classic results, due to K. Doerk and P. Hall respectively, establish the solvability of those finite groups all of whose maximal subgroups are supersolvable, and the solvability of finite groups in which all maximal subgroups have prime or squared prime index. In this note we describe the structure of the non-solvable finite groups whose maximal subgroups are either supersolvable or have prime or squared prime index.