The Reidemeister spectrum of split metacyclic groups

Abstract

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

34 pages, rewritten section 2.2 and parts of section 4 for clarity; added references for technical results; results are unchanged

References in corpus (1)

• The Reidemeister spectra of low dimensional crystallographic groups