Factorizations of almost simple groups with a factor having many nonsolvable composition factors

TL;DR

This paper classifies factorizations of almost simple groups where one factor has multiple nonsolvable composition factors, simplifying the broader factorization problem by reducing it to cases with a single nonsolvable factor.

Contribution

The authors provide a classification of certain group factorizations, advancing the understanding of the structure of almost simple groups with complex factors.

Findings

Classified factorizations with a factor having at least two nonsolvable composition factors

Reduced the general factorization problem to cases with a single nonsolvable composition factor

Extended previous classification results to broader group structures

Abstract

This paper classifies the factorizations of almost simple groups with a factor having at least two nonsolvable composition factors. This together with a previous classification result of the authors reduces the factorization problem of almost simple groups to the case where both factors have a unique nonsolvable composition factor.