Kronecker classes and cliques in derangement graphs

2025/02/03 by Cazzola, Marina, Gogniat, Louis, Spiga, Pablo · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2502.01287

Abstract

Given a permutation group G, the derangement graph of G is defined with vertex set G, where two elements x and y are adjacent if and only if xy^-1 is a derangement. We establish that, if G is transitive with degree exceeding 30, then the derangement graph of G contains a complete subgraph with four vertices. As a consequence, if G is a normal subgroup of A such that |A : G| = 3, and if U is a subgroup of G satisfying G = \bigcup_{a ∈ A} U^a, then |G : U| ≤ 10. This result provides support for a conjecture by Neumann and Praeger concerning Kronecker classes.

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