Automorphism groups of metacyclic groups of class two

Abstract

An automorphism of a group G is an isomorphism from G to G, which is one to one, onto and preserving operation. The automorphism of G forms a group under composition, and is denoted as Aut ?G?. A group is metacyclic if there is a normal cyclic subgroup whose quotient group is also cyclic. In 1973, King classified metacyclic p ? group while in 1987, Newman developed a new approach to metacyclic p ? groups suggested by the p ? group generation algorithm. They found new presentation for these groups. The automorphism groups can be separated to inner and outer automorphisms. An inner automorphism is an automorphism corresponding to conjugation by some element a. The set of all automorphisms form a normal subgroup of Aut ?G?. The automorphism group which is not inner is called outer automorphism and denoted as Out ?G?. In this research, automorphism groups of split and non-split metacyclic groups of class two will be investigated including the inner and outer automorphisms.