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Conjugacy Separability of Certain Free Products with Amalgamation

Peter F. Stebe
Transactions of the American Mathematical Society
Vol. 156 (May, 1971), pp. 119-129
DOI: 10.2307/1995602
Stable URL: http://www.jstor.org/stable/1995602
Page Count: 11
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Conjugacy Separability of Certain Free Products with Amalgamation
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Abstract

Let $G$ be a group. An element $g$ of $G$ is called conjugacy distinguished or 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 $\xi(h)$ and $\xi(g)$ are not conjugate in $\xi(G)$. Following A. Mostowski, a group $G$ is conjugacy separable or c.s. if and only if every element of $G$ is c.d. in $G$. In this paper we prove that every element conjugate to a cyclically reduced element of length greater than 1 in the free product of two free groups with a cyclic amalgamated subgroup is c.d. We also prove that a group formed by adding a root of an element to a free group is c.s.

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