Analysis of generating minimally transitive permutation groups

Abstract

A transitive permutation group G ≤ Sn is called minimally transitive if every proper subgroup of G is intransitive. In this paper, we consider the minimal number of elements d(G)required to generate such a group G, in terms of its degree n. For the prime factorization n =p prime pn(p) of n, we will write ω(n):= p n(p) and μ(n) : = max{n(p) : p prime}.