Abstract Given a group G and an automorphism of G, two elements x, y G are said to be -conjugate if x=gy (g) ^-1 for some g G. The number R () of equivalence classes with respect to this relation is called the Reidemeister number of and the set \R () {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.
Marius Tărnăuceanu (Mon,) studied this question.