Conjugacy separability of certain free products with amalgamation

Stebe, Peter F.

doi:10.1090/S0002-9947-1971-0274597-5

Conjugacy separability of certain free products with amalgamation
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by Peter F. Stebe

Trans. Amer. Math. Soc. 156 (1971), 119-129

DOI: https://doi.org/10.1090/S0002-9947-1971-0274597-5

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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.

References

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Combinatorial group theory

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Theorie der Gruppen von endlicher Ordnung

P. F. Stebe, A residual property of certain groups, Proc. Amer. Math. Soc. 26 (1970), 37–42. MR 260874, DOI 10.1090/S0002-9939-1970-0260874-5