THE REIDEMEISTER SPECTRUM OF ZM-GROUPS
Abstract
Abstract Given a group G and an automorphism $\varphi $ of G , two elements $x,y\in G$ are said to be $\varphi $ -conjugate if $x=gy\varphi (g)^{-1}$ for some $g\in G$ . The number $R(\varphi )$ of equivalence classes with respect to this relation is called the Reidemeister number of $\varphi $ and the set $\{R(\varphi ) \mid \varphi \in \text {Aut}(G)\}$ is called the Reidemeister spectrum of G . We determine the Reidemeister spectrum of ZM-groups, extending some results of Senden [‘The Reidemeister spectrum of split metacyclic groups’, Preprint, 2022, arXiv:2109.12892].
Fields of Study & Subjects
Finite Group Theory Research
Geometric and Algebraic Topology
Rings
Modules
and Algebras
Publication details
- Journal / source
- Bulletin of the Australian Mathematical Society
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–6
- Publication date
- 12 January 2026
- Language
- EN