Large subgroups of simple groups

2013/11/26 by Seyed Hassan Alavi, Alavi, S. Hassan, Timothy C. Burness +1 · 5 citations
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1311.6733

openalex publication_date 2013/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group. A proper subgroup H of G is said to be large if the order of H satisfies the bound |H|³ ≥ |G|. In this note we determine all the large maximal subgroups of finite simple groups, and we establish an analogous result for simple algebraic groups (in this context, largeness is defined in terms of dimension). An application to triple factorisations of simple groups (both finite and algebraic) is discussed.

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