Conjugate generation of sporadic almost simple groups

2025/05/08 by Д. О. Ревин, Revin, Danila O., Andrei V. Zavarnitsine +1
Mathematics · #20D08 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2505.05173

openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As defined by Guralnick and Saxl, given a nonabelian simple group S and its nonidentity automorphism x, a natural number α_S(x) is the minimum number of conjugates of x in ⟨ x,S⟩ that generate a subgroup containing S. In this paper, for every sporadic group S other than the Monster and an automorphism x of S of prime order, we complete the determination of the precise value of α_S(x).

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