Transitive permutation groups with bounded movement having maximal degree (Q1283279)

The fourth author has shown that if \(G\) is a transitive permutation group on a set \(\Omega\) which is not a 2-group, and there is a positive integer \(m\) such that \(|\Gamma^g\setminus\Gamma|\leq m\) for all \(\Gamma\subseteq\Omega\) and \(g\in G\), then \(|\Omega|\) is at most the integer part of \(2mp/(p-1)\), where \(p\) is the least odd prime dividing \(| G|\). Here, permutation groups attaining the bound are described.