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CONJUGACY SEPARABILITY OF CERTAIN GENERALIZED FREE PRODUCTS OF NILPOTENT GROUPS

  • Kim, Goansu ;
  • Tang, C.Y.
  • Received : 2011.07.04
  • Published : 2013.07.01

Abstract

It is known that generalized free products of finitely generated nilpotent groups are conjugacy separable when the amalgamated subgroups are cyclic or central in both factor groups. However, those generalized free products may not be conjugacy separable when the amalgamated subgroup is a direct product of two infinite cycles. In this paper we show that generalized free products of finitely generated nilpotent groups are conjugacy separable when the amalgamated subgroup is ${\langle}h{\rangle}{\times}D$, where D is in the center of both factors.

Keywords

generalized free products;residually finite;conjugacy separable;nilpotent groups

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Acknowledgement

Supported by : NRF, Natural Science and Engineering Research Council of Canada