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Separating conjugates in amalgamated free products and HNN extensions

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Joan L. Dyer
Joan L. Dyer
Affiliation:
Lehman college and the Graduate CenterC.U.N.Y. New York, U.S.A.
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Abstract

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A group G is termed conjugacy separable (c.s.) if any pair of distinct conjugacy classes may be mapped to distinct conjugacy classes in some finite epimorph of G. The free product of A and B with cyclic amalgamated subgroup H is shown to be c.s. if A and B are both free, or are both finitely generated nilpotent groups. Further, one-relator groups with nontrivial center and HNN extensions with c.s. base group and finite associated subgroups are also c.s.

MSC classification

Secondary: 20E26: Residual properties and generalizations; residually finite groups 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20F10: Word problems, other decision problems, connections with logic and automata
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 1 , February 1980 , pp. 35 - 51
Copyright
Copyright © Australian Mathematical Society 1980

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