2021
DOI: 10.1080/00927872.2021.1945615
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Twisted conjugacy in direct products of groups

Abstract: Given a group G and an endomorphism ϕ of G, two elements x, y ∈ G are said to be ϕ-conjugate if x = gyϕ(g) −1 for some g ∈ G. The number of equivalence classes for this relation is the Reidemeister number R(ϕ) of ϕ. The set {R(ψ) | ψ ∈ 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.

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Cited by 7 publications
(2 citation statements)
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“…In order to study the endomorphisms of a direct product, we introduce some notation (which coincides with the notation from [Sen21]).…”
Section: The Second Method: Simplicial Joinmentioning
confidence: 99%
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“…In order to study the endomorphisms of a direct product, we introduce some notation (which coincides with the notation from [Sen21]).…”
Section: The Second Method: Simplicial Joinmentioning
confidence: 99%
“…, d r−1 )) such that R(ψ) = 2. Since Spec R (Z 3 ) = N >0 ∪ {∞} (see for example [Rom11, Section 3]), we can fix some ψ ′ ∈ Aut(Z 3 ) such that R(ψ ′ ) = k. By Proposition 2.4 in [Sen21] it follows that the automorphism…”
Section: By Taking For Example Kmentioning
confidence: 99%