A residual property of certain groups

Author:
P. F. Stebe

Journal:
Proc. Amer. Math. Soc. **26** (1970), 37-42

MSC:
Primary 20.48

MathSciNet review:
0260874

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Abstract: An element of a group is called conjugacy distinguished or c.d. in if and only if given any element of either is conjugate to or there is a homomorphism from onto a finite group such that and are not conjugate in . Following A. Mostowski, a group is called conjugacy separable or c.s. if every element of is c.d. A. Mostowski remarks that a direct product of c.s. groups is c.s. and proves that the conjugacy problem can be solved for finitely presented c.s. groups. N. Blackburn proves that finitely generated nilpotent groups are c.s. In this paper it is proven that a free product of c.s. groups is c.s., a free group is c.s. and that every element of infinite order in a finite extension of a free group is c.d.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1970-0260874-5

Keywords:
Group,
c. s. group,
residual property,
conjugacy problem

Article copyright:
© Copyright 1970
American Mathematical Society