Orbits of Permutation Groups on Unordered Sets, III: Imprimitive Groups
Peter J. Cameron · Journal of the London Mathematical Society · 1983
This paper studies imprimitive groups G having a finite number nk(G) of orbits on k-sets for all k. The main results are a formula for nk(G Wr H) in terms of nk(G) and a ‘modified cycle index’ of H, and relations between the growth rate of (nk(G)) and the structure of primitive components of G.