Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups
Let φ : G → G be a group endomorphism where G is a finitely generated group of exponential growth, and denote by R(φ) the number of twisted φ-conjugacy classes. Fel’shtyn and Hill [7] conjectured that if φ is injective, then R(φ) is infinite. This conjecture is true for automorphisms of non-elem...
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| Дата: | 2006 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2006
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/157372 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups / A. Fel’shtyn, D.L. Goncalves // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 3. — С. 36–48. — Бібліогр.: 22 назв. — англ. |
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irk-123456789-1573722019-06-21T01:27:49Z Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups Fel’shtyn, A. Goncalves, D.L. Let φ : G → G be a group endomorphism where G is a finitely generated group of exponential growth, and denote by R(φ) the number of twisted φ-conjugacy classes. Fel’shtyn and Hill [7] conjectured that if φ is injective, then R(φ) 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 6= 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 6= n. 2006 Article Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups / A. Fel’shtyn, D.L. Goncalves // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 3. — С. 36–48. — Бібліогр.: 22 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 20E45, 37C25, 55M20. http://dspace.nbuv.gov.ua/handle/123456789/157372 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Let φ : G → G be a group endomorphism where
G is a finitely generated group of exponential growth, and denote
by R(φ) the number of twisted φ-conjugacy classes. Fel’shtyn and
Hill [7] conjectured that if φ is injective, then R(φ) 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 6= 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 6= n. |
| format |
Article |
| author |
Fel’shtyn, A. Goncalves, D.L. |
| spellingShingle |
Fel’shtyn, A. Goncalves, D.L. Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups Algebra and Discrete Mathematics |
| author_facet |
Fel’shtyn, A. Goncalves, D.L. |
| author_sort |
Fel’shtyn, A. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/157372 |
| citation_txt |
Twisted conjugacy classes of Automorphisms of Baumslag-Solitar groups / A. Fel’shtyn, D.L. Goncalves // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 3. — С. 36–48. — Бібліогр.: 22 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT felshtyna twistedconjugacyclassesofautomorphismsofbaumslagsolitargroups AT goncalvesdl twistedconjugacyclassesofautomorphismsofbaumslagsolitargroups |
| first_indexed |
2023-05-20T17:51:51Z |
| last_indexed |
2023-05-20T17:51:51Z |
| _version_ |
1796154275357786112 |