The Reidemeister spectrum of ZM-groups

Given a group $G$ and an automorphism $φ$ of $G$, two elements $x,y\in G$ are said to be $φ$-conjugate if $x=gyφ(g)^{-1}$ for some $g\in G$. The number $R(φ)$ of equivalence classes with respect to this relation is called the Reidemeister number of $φ$ and the set $\{R(φ)|φ\in {\rm Aut}(G)\}$ is called the Reidemeister spectrum of $G$. In this paper, we determine the Reidemeister spectrum of ZM-groups, extending some results of \cite{13}.

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