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 from *G* onto a finite group such that and are not conjugate in . 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:
http://dx.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