Conjugacy separating representations of free groups

Wehrfritz, B. A. F.

doi:10.1090/S0002-9939-1973-0374269-X

Conjugacy separating representations of free groups
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Proc. Amer. Math. Soc. 40 (1973), 52-56 Request permission

Abstract:

If $G$ is a free group and $g$ is an element of $G$ we show that there exists a residually finite (commutative) integral domain $R$ and a faithful matrix representation $\rho$ of $G$ over $R$ of finite degree such that the conjugacy class of $g\rho$ in $G\rho$ is closed in the topology induced on $G\rho$ by the Zariski topology on the full matrix algebra. It follows that free groups are conjugacy separable, a result obtained by a number of authors, see [1], [5] and [6].

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