This paper shows that if H and K are finite groups with no common direct factor and G = H × K, then the structure and order of Aut G can be simply expressed in terms of Aut H , Aut K and the central homomorphism groups Hom (H, Z(K)) and Hom (K, Z(H )).

This paper finds the order, structure and presentation for the automorphism group of a split metacyclic p-group, where p is odd.

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In this paper we first find the automorphism group of the direct product of n copies of an indecomposable non-abelian group. We describe the automorphism group as matrices with entries which are homomorphisms between the n direct factors. We then use this description with a generalization of a result by Bidwell, Curran, and McCaughan on Aut (H ×K), where H and K have no common direct factor, to provide structure and order theorems for an arbitrary direct product.

We clarify the definition of the subgroup C given in the paper, correct Theorem 3.2, Lemma 4.1 and the presentation of the automorphism group of a split metacyclic p-group given in Theorem 4.2.In the paper [1] we considered the automorphism group of a nonabelian split metacyclic p-groupwhere p was odd, m ≥ 2, n ≥ 1 and 1 ≤ r ≤ min{m − 1, n}. For convenience three cases were considered:Zhou and Liu [4] have pointed out some errors in Theorem 3.2, Lemma 4.1, and Theorem 4.2 of our paper and we are grateful for their observation. The errors arose because of some poor notation associated with our automorphism c, so here we clarify its definition and correct these results. Throughout this note for group elements g and h, g h denotes h −1 gh.