1. Let E be a finite non-null set and write (E) for the family of all permutations of E. Let be a non-null subset of (E) and write () for the subgroup of (E) generated by the members of . For any α ∈ we putso that () is a subgroup of () and is independent of the choice of α in . We suppose that E splits into k disjoint transitivity sets (orbits) E_i(1 ≤ i ≤ k) with respect to (); thus σE_i = E_i for all σ ∈ ().