The Reidemeister spectrum of split metacyclic groups

2021/09/27 by Pieter Senden, Senden, Pieter
Mathematics · #20D45 #20E45 (Primary) 20E22 (Secondary) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2109.12892

openalex publication_date 2021/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a group G and an automorphism φ of G, two elements x, y ∈ G are said to be φ-conjugate if x = gy φ(g)^-1 for some g ∈ G. The number of equivalence classes for this relation is the Reidemeister number R(φ) of φ. The set \R(ψ) | ψ∈ Aut(G)\ is called the Reidemeister spectrum of G. We fully determine the Reidemeister spectrum of split metacyclic groups of the form C_n \rtimes C_p where p is a prime and the action is non-trivial.

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