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Transactions of the American Mathematical Society

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

 

 

Conjugacy separability of certain free products with amalgamation


Author: Peter F. Stebe
Journal: Trans. Amer. Math. Soc. 156 (1971), 119-129
MSC: Primary 20.52
MathSciNet review: 0274597
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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 $ from G onto a finite group such that $ \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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DOI: https://doi.org/10.1090/S0002-9947-1971-0274597-5
Keywords: Group, conjugacy problem, conjugacy separable group, free product with amalgamation
Article copyright: © Copyright 1971 American Mathematical Society