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Conjugacy separability of certain Fuchsian groups


Author: P. F. Stebe
Journal: Trans. Amer. Math. Soc. 163 (1972), 173-188
MSC: Primary 20H10; Secondary 10D05
DOI: https://doi.org/10.1090/S0002-9947-1972-0292949-5
MathSciNet review: 0292949
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Abstract: Let $ G$ be a group. An element $ g$ is c.d. in $ G$ if and only if given any element $ h$ of $ G$, either it is conjugate to $ h$ or there is a homomorphism $ \xi $ from $ G$ onto a finite group such that $ \xi (g)$ is not conjugate to $ \xi (h)$. Following A. Mostowski, a group is conjugacy separable or c.s. if and only if every element of the group is c.d. Let $ F$ be a Fuchsian group, i.e. let $ F$ be presented as

$\displaystyle F = ({S_1}, \ldots ,{S_n},{a_1}, \ldots ,{a_{2r}},{b_1}, \ldots ,... ..._n}{a_1} \ldots {a_{2r}}a_1^{ - 1} \ldots a_{2r}^{ - 1}{b_1} \ldots {b_t} = 1).$

In this paper, we show that every element of infinite order in $ F$ is c.d. and if $ t \ne 0$ or $ r \ne 0$, $ F$ is c.s.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0292949-5
Keywords: Group, conjugacy separable group, Fuchsian group, conjugacy problem
Article copyright: © Copyright 1972 American Mathematical Society

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