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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Conjugacy separability of the groups of hose knots


Author: Peter F. Stebe
Journal: Trans. Amer. Math. Soc. 159 (1971), 79-90
MSC: Primary 20.10
MathSciNet review: 0285590
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Abstract: Let $ G$ be a group. An element $ g$ of $ G$ is c.d. in $ G$ if and only if, given any element $ h$ of $ G$, either $ h$ is conjugate to $ g$ 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. In this paper we show that the groups of hose knots are c.s.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0285590-0
Keywords: Group, conjugacy, separable group, conjugacy problem, knot group
Article copyright: © Copyright 1971 American Mathematical Society