Inner automorphisms and some their generalizations

In the first part of this paper we provides an overview of some of the results for normal, quasi-inner, polynomial, power automorphisms of groups. Each of these automorphisms generalizes the notion of an inner automorphism in certain direction. The second part of the work associated with the classical braid group. Here are the results on the structure of the normal automorphism groups of braid groups and pure braid groups. Also we give the assertion that the center of the pure braid groups is a direct factor, and give the new system generators of braid groups.