A classification of metacyclic groups by group invariants

2023/01/20 by Àngel García-Blázquez, Ángel del Rı́o, García-Blázquez, Àngel +1
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2301.08683

openalex publication_date 2023/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm which computes all the metacyclic groups of a given order. A GAP implementation of these algorithms is given.

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