Near permutation semigroups

A transformation semigroup over a set X with N elements is said to be a near permutation semigroup if it is generated by a group of permutations on N elements and by a set of transformations of rank N-1. In this paper we make a summary of the author's thesis, in which are exhibited ways of checking whether those specific transformation semigroups belong to various structural classes of semigroups, just by analysis of the generators and without first having to generate them.