Automorphisms of \(p\)-groups with cyclic commutator subgroup
This paper contains a systematic study of the automorphism groups of finite, non abelian, 2-generated \(p\)-groups with cyclic commutator subgroup for odd primes \(p\). First the metacyclic groups are considered and then the non metacyclic groups are analysed in relation to the nontrivial direct factors of \(G/G'\) contained in \(C_ G(G')/G'\). For each case the orders of \(\text{Aut}(G)\), \(O_ p(\text{Aut}(G))\) and \(C_{\text{Aut}(G)}(G/\Phi(G))\) are computed. In many instances the effect of \(\text{Aut}(G)\) on two choosen generators of \(G\) is displayed.
scientific article; zbMATH DE number 510100