J. Aust. Math. Soc.  74 (2003), 287-294
On permutation groups with constant movement

Mehdi Alaeiyan (Khayaty)
  Department of Mathematics
  Iran University of Science and Technology
  Narmak, Tehran 16844

Let $G$ be a permutation group on a set $\Omega$ with no fixed point in $\Omega$. If for each subset $\Gamma$ of $\Omega$ the size $|\Gamma^g-\Gamma|$ is bounded, for $g\in G$, we define the movement of $g$ as the max $|\Gamma^g-\Gamma|$ over all subsets $\Gamma$ of $\Omega$. In particular, if all non-identity elements of $G$ have the same movement, then we say that $G$ has constant movement. In this paper we will first give some families of groups with constant movement. We then classify all transitive permutation groups with a given constant movement $m$ on a set of maximum size.
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