2024/04/29 by Hong Yi Huang, Cai Heng Li, Huang, Hong Yi +3
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #Coding theory and cryptography #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2404.18753
Let G\leqslantSym(Ω) be a finite transitive permutation group with point stabiliser H. We say that a subgroup K of G is a fixer if every element of K has fixed points, and we say that K is large if |K| \geqslant |H|. There is a special interest in studying large fixers due to connections with Erdős-Ko-Rado type problems. In this paper, we classify up to conjugacy the large fixers of the almost simple primitive groups with socle PSL2(q), and we use this result to verify a special case of a conjecture of Spiga on permutation characters. We also present some results on large fixers of almost simple primitive groups with socle an alternating or sporadic group.