Intransitive permutation group with bounded movement. (Q1413416)

Let \(G\) be a permutation group on a set \(\Omega\). The movement of \(G\) is the number \[ m=\max_{\Gamma\subset\Omega} \max_{g\in G} |\Gamma^g-\Gamma|. \] If \(m\) is finite, then \(G\) is said to have bounded movement. In this paper, the authors construct a family of finite permutation groups \(G\) of degree \(n\) such that the movement of \(G\) is close to \([n(p-1)/2p]\), where \(p\) is the smallest prime divisor of \(| G|\).