A classification of the finite two-generated cyclic-by-abelian groups of\n prime power order

We obtain a classification of the finite two-generated cyclic-by-abelian\ngroups of prime-power order. For that we associate to each such group $G$ a\nlist $\\inv(G)$ of numerical group invariants which determines the isomorphism\ntype of $G$. Then we describe the set formed by all the possible values of\n$\\inv(G)$. This allows computer implementations for constructing all the\nfinite-two generated cyclic-by-abelian groups of a given prime-power order,\ncomputing the invariants of such a group, and to decide whether two such groups\nare isomorphic.\n