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THE REIDEMEISTER SPECTRUM OF ZM-GROUPS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 114 / Issue 1 / August 2026
- Published online by Cambridge University Press:
- 12 January 2026, pp. 101-106
- Print publication:
- August 2026
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- Article
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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].
