J. Aust. Math. Soc.
74 (2003), 287294

On permutation groups with constant movement


Abstract

Let
be a permutation group on a set
with no fixed point in
. If for each subset
of
the size
is bounded, for
, we define the movement of
as the max
over all subsets
of
. In particular, if all nonidentity elements of
have the same movement, then we say that
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
on a set of maximum size.

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