Large maximal subgroups of almost simple classical groups

TL;DR

This paper classifies all large maximal subgroups of almost simple classical groups, completing the broader classification of large maximal subgroups in almost simple groups by building on prior foundational work.

Contribution

It provides a complete classification of all large maximal subgroups of almost simple classical groups, extending previous partial results.

Findings

Identified all large maximal subgroups of almost simple classical groups.

Completed the classification of large maximal subgroups in almost simple groups.

Built on prior work to finalize the classification effort.

Abstract

A proper subgroup $H$ in a finite group $G$ is said to be large if $|H|^3\geq |G|$. In this paper, we determined all large maximal subgroups of almost simple classical groups. Combined with the work of Alavi and Burness (J. Algebra 421 (2015) 187--233) and Alavi, Bayat, and Daneshkhah (J. Algebraic Combin. 55 (2022) 729--779), this completes the classification of all large maximal subgroups of almost simple groups.