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.