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

2021/06/11 by Osnel Broche, Diego R. García, Broche, Osnel +4
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Mathematics and Applications #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2106.06449

openalex publication_date 2021/06/11 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

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

Citations

• The Modular Isomorphism Problem for small groups -- revisiting Eick's algorithm

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