No abstract

No abstract

No abstract

We determine all primitive groups which do not have a regular orbit on the power set of the permutation domain. As a corollary, we also determine all families of orbit equivalent primitive permutation groups. Cameron, Neumann, and Saxl [1] proved that there is a constant M such that if n M and G S n is a primitive permutation group not containing A n , then G has a regular orbit on the power set of the permutation domain. Recently, in investigations of the minimal base size of primitive groups [5, 6], an explicit bound was needed. It turns out that it is not hard to determine all the exceptions. For brevity, we shall say that G S n satisfies the condition (NR) if G is primitive, does not contain A n , and has no regular orbits on the power set. Clearly, the last condition means that no subset of the permutation domain has trivial set stabilizer. T 1. The only alues of n for which there exist G S n satisfying (NR) are 5 n 17, 21 n 24 and n l 32.