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Transitive permutation groups with elements of movement $$m$$ or $$m-1$$. (English) Zbl 1289.20001
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 $$m-1$$.
##### MSC:
 20B05 General theory for finite permutation groups 20B20 Multiply transitive finite groups