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- Title
Twisted conjugacy classes in unitriangular groups.
- Authors
Nasybullov, Timur
- Abstract
Let R be an integral domain of characteristic zero. In this note we study the Reidemeister spectrum of the group UTn(R) of unitriangular matrices over R. We prove that if R+ is finitely generated and n > 2 |R*|, then UTn(R) possesses the R∞-property, i.e. the Reidemeister spectrum of UTn(R) contains only ∞, however, if n ≤ |R *|, then the Reidemeister spectrum of UTn(R) has nonempty intersection with ℕ. If R is a field and n ≥ 3, then we prove that the Reidemeister spectrum of UTn(R) coincides with {1 , ∞}, i.e. in this case UTn(R) does not possess the R∞-property.
- Subjects
CONJUGACY classes; INTEGRAL domains; MATRICES (Mathematics); AUTOMORPHISMS; HOMEOMORPHISMS
- Publication
Journal of Group Theory, 2019, Vol 22, Issue 2, p253
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2018-0127