The binary actions of simple groups with a single conjugacy class of involutions

2024/02/03 by Nick Gill, Gill, Nick, Pierre Guillot +1
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2402.02269

openalex publication_date 2024/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We continue our investigation of binary actions of simple groups. In this paper, we demonstrate a connection between the graph Γ(C) based on the conjugacy class C of the group G, which was introduced in our previous work, and the notion of a strongly embedded subgroup of G. We exploit this connection to prove a result concerning the binary actions of finite simple groups that contain a single conjugacy class of involutions.

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