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

Osnel Broche; Diego García; Ángel del Río

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arXiv · 2106.06449

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

Osnel Broche·Diego García·Ángel del Río

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Abstract

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

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Osnel Broche, Diego García, Ángel del Río. 2021-06-11. A classification of the finite two-generated cyclic-by-abelian groups of prime power order. https://arxiv.org/abs/2106.06449

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