### Extending the concept of a t-homogeneous permutation group

Alex Dent
*Royal Holloway*

If a group acts on a set such that any subset of $t$ points can be mapped
to any other subset of $t$ points then the group is said to be acting
$t$-homogeneously. A group that acts $t$-homogeneously is necessarily
transitive. This talk investigates how this concept can be extended to
groups that act non-transitively on sets.