In this paper we give answers to some open questions concerning generation
and enumeration of finite transitive permutation groups. In [1],
Bryant, Kovács and Robinson proved that there is a number c′such that each soluble transitive permutation group of degree n [ges ] 2 can be
generated by [c′ n/ √log n]
elements, and later A. Lucchini [5] extended this result
(with a different constant c′) to finite
permutation groups containing a soluble transitive subgroup. We are now able to
prove this theorem in full generality, and this solves the question of bounding the
number of generators of a finite transitive permutation group in terms of its degree.
The result obtained is the following.