Derangements in primitive permutation groups, with an application to\n character theory

2014/03/29 by Timothy C. Burness, Burness, Timothy C., Hung P. Tong‐Viet +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1403.7666

openalex publication_date 2014/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite primitive permutation group and let \κ(G) be the\nnumber of conjugacy classes of derangements in G. By a classical theorem of\nJordan, \κ(G) geqslant 1. In this paper we classify the groups G with\n\κ(G)=1, and we use this to obtain new results on the structure of finite\ngroups with an irreducible complex character that vanishes on a unique\nconjugacy class. We also obtain detailed structural information on the groups\nwith \κ(G)=2, including a complete classification for almost simple\ngroups.\n

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