Twisted Conjugacy in Direct Products of Groups

Abstract

Given a group $G$ and an endomorphism $\phi$ 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 investigate Reidemeister numbers and spectra on direct products of finitely many groups and determine what information can be derived from the individual factors.

arXiv commentAccepted manuscript

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Cited by in corpus (2)

• Thompson-like groups, Reidemeister numbers, and fixed points
• The R${}_{\infty }$-property for braid groups over orientable surfaces