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

Gill, Nick and Guillot, Pierre (2025). The binary actions of simple groups with a single conjugacy class of involutions. Journal of Group Theory, 28(1) pp. 215–240.

DOI: https://doi.org/10.1515/jgth-2024-0066

Abstract

We continue our investigation of binary actions of simple groups. In this paper, we demonstrate a connection between the graph $\Gamma(C)$ 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.