an:06255441
Zbl 1289.20001
Alaeiyan, Mehdi; Askari, Bahman
Transitive permutation groups with elements of movement \(m\) or \(m-1\)
EN
Math. Rep., Bucur. 14(64), No. 4, 317-324 (2012).
00329079
2012
j
20B05 20B20
transitive permutation groups; groups of bounded movement; fixed point free elements
Summary: Let \(G\) be a permutation group on a set \(\Omega\) with no fixed point in \(\Omega\) and let \(m\) be a positive integer. If for each subset \(\Gamma\) of \(\Omega\) the size \(|\Gamma^g\setminus\Gamma|\) is bounded, for \(g\in G\), we define the movement of \(g\) as the matrix \(|\Gamma^g\setminus\Gamma|\) over all subsets \(\Gamma\) of \(\Omega\), and the movement of \(G\) is defined as the maximum of \(\text{move}(g)\) over all non-identity elements of \(g\in G\). In this paper we will classify all transitive permutation groups \(G\) with bounded movement equal to \(m\), such that \(G\) is not a 2-group but in which every non-identity element has the movement \(m\) or \(m-1\).