Solvable intransitive permutation groups with constant movement

Abstract

Abstract Let \(G\) be a permutation group on a set \({\Omega }\) without any fixed points in \({\Omega }\). If for \(g\in G\) and for each subset \({\Gamma }\) of \({\Omega }\) the size \(|{{\Gamma }}^{g}-{\Gamma }|\) is bounded, then we define the movement of \(g\) as move\(\left(g\right):={\text{s}\text{u}\text{p}}_{{\Gamma }}|{{\Gamma }}^{g}-{\Gamma }|\). If for every non-identity elements \(g\) and \(h\) of \(G\), move\(\left(g\right)\)=move\(\left(h\right)\), then we say that \(G\) has constant movement. In this paper, we classify all solvable intransitive permutation groups with constant movement.