The binary actions of simple groups of Lie type of characteristic 2

2024/02/13 by Gill, Nick, Guillot, Pierre, Liebeck, Martin W.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2402.08357

Abstract

Let C be a conjugacy class of involutions in a group G. We study the graph Γ(C) whose vertices are elements of C with g,h\inC connected by an edge if and only if gh\inC. For t∈ C, we define the component group of t to be the subgroup of G generated by all vertices in Γ(C) that lie in the connected component of the graph that contains t. We classify the component groups of all involutions in simple groups of Lie type over a field of characteristic 2. We use this classification to partially classify the transitive binary actions of the simple groups of Lie type over a field of characteristic 2 for which a point stabilizer has even order. The classification is complete unless the simple group in question is a symplectic or unitary group.

Related

• The binary actions of simple groups with a single conjugacy class of involutions
• The binary actions of alternating groups
• Characteristic classes of involutions in nonsolvable groups
• Automorphism Groups of the PSL₂(q) Commuting Involution Graphs
• Commuting involutions and elementary abelian subgroups of simple groups