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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Conjugacy separating representations of free groups


Author: B. A. F. Wehrfritz
Journal: Proc. Amer. Math. Soc. 40 (1973), 52-56
MSC: Primary 20E05
DOI: https://doi.org/10.1090/S0002-9939-1973-0374269-X
MathSciNet review: 0374269
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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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DOI: https://doi.org/10.1090/S0002-9939-1973-0374269-X
Keywords: Free groups, conjugacy separable, faithful representations
Article copyright: © Copyright 1973 American Mathematical Society