Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups
Let \(\phi:G \to G\) be a group endomorphism where \(G\) is a finitely generated group of exponential growth, and denote by \(R(\phi)\) the number of twisted \(\phi\)-conjugacy classes. Fel'shtyn and Hill [7] conjectured that if \(\phi\) is injective, then \(R(\phi)\) is infinite. This conjectu...
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-8962018-03-21T07:07:28Z Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups Fel’shtyn, Alexander Goncalves, Daciberg L. Reidemeister number, twisted conjugacy classes, Baumslag-Solitar groups 20E45, 37C25, 55M20 Let \(\phi:G \to G\) be a group endomorphism where \(G\) is a finitely generated group of exponential growth, and denote by \(R(\phi)\) the number of twisted \(\phi\)-conjugacy classes. Fel'shtyn and Hill [7] conjectured that if \(\phi\) is injective, then \(R(\phi)\) is infinite. This conjecture is true for automorphisms of non-elementary Gromov hyperbolic groups, see [17] and [6]. It was showed in [12] that the conjecture does not hold in general. Nevertheless in this paper, we show that the conjecture holds for injective homomorphisms for the family of the Baumslag-Solitar groups \(B(m,n)\) where \(m\ne n\) and either \(m\) or \(n\) is greater than 1, and for automorphisms for the case \(m=n>1\). family of the Baumslag-Solitar groups \(B(m,n)\) where \(m\ne n\). Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/896 Algebra and Discrete Mathematics; Vol 5, No 3 (2006) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/896/425 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-03-21T07:07:28Z |
| collection |
OJS |
| language |
English |
| topic |
Reidemeister number twisted conjugacy classes Baumslag-Solitar groups 20E45 37C25 55M20 |
| spellingShingle |
Reidemeister number twisted conjugacy classes Baumslag-Solitar groups 20E45 37C25 55M20 Fel’shtyn, Alexander Goncalves, Daciberg L. Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups |
| topic_facet |
Reidemeister number twisted conjugacy classes Baumslag-Solitar groups 20E45 37C25 55M20 |
| format |
Article |
| author |
Fel’shtyn, Alexander Goncalves, Daciberg L. |
| author_facet |
Fel’shtyn, Alexander Goncalves, Daciberg L. |
| author_sort |
Fel’shtyn, Alexander |
| title |
Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups |
| title_short |
Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups |
| title_full |
Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups |
| title_fullStr |
Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups |
| title_full_unstemmed |
Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups |
| title_sort |
twisted conjugacy classes of automorphisms of baumslag-solitar groups |
| description |
Let \(\phi:G \to G\) be a group endomorphism where \(G\) is a finitely generated group of exponential growth, and denote by \(R(\phi)\) the number of twisted \(\phi\)-conjugacy classes. Fel'shtyn and Hill [7] conjectured that if \(\phi\) is injective, then \(R(\phi)\) is infinite. This conjecture is true for automorphisms of non-elementary Gromov hyperbolic groups, see [17] and [6]. It was showed in [12] that the conjecture does not hold in general. Nevertheless in this paper, we show that the conjecture holds for injective homomorphisms for the family of the Baumslag-Solitar groups \(B(m,n)\) where \(m\ne n\) and either \(m\) or \(n\) is greater than 1, and for automorphisms for the case \(m=n>1\). family of the Baumslag-Solitar groups \(B(m,n)\) where \(m\ne n\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/896 |
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AT felshtynalexander twistedconjugacyclassesofautomorphismsofbaumslagsolitargroups AT goncalvesdacibergl twistedconjugacyclassesofautomorphismsofbaumslagsolitargroups |
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2025-07-17T10:32:10Z |
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2025-07-17T10:32:10Z |
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1837889833601597440 |