RUS  ENG
Полная версия
ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2006, выпуск 3, страницы 36–48 (Mi adm269)

Эта публикация цитируется в 8 статьях

RESEARCH ARTICLE

Twisted conjugacy classes of Automorphisms of Baumslag–Solitar groups

Alexander Fel'shtyna, Daciberg L. Gonçalvesb

a Instytut Matematyki, Uniwersytet Szczecinski, ul. Wielkopolska 15, 70–451 Szczecin, Poland and Boise State University, 1910 University Drive, Boise, Idaho, 83725–155, USA
b Dept. de Matemática – IME – USP, Caixa Postal 66.281 –CEP 05311–970, São Paulo –SP, Brasil

Аннотация: 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 $m\ne n$.

Ключевые слова: Reidemeister number, twisted conjugacy classes, Baumslag–Solitar groups.

MSC: 20E45, 37C25, 55M20

Поступила в редакцию: 30.01.2006
Исправленный вариант: 24.11.2006

Язык публикации: английский



Реферативные базы данных:


© МИАН, 2024