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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A converse to a residual finiteness theorem of G. Baumslag


Author: M. Shirvani
Journal: Proc. Amer. Math. Soc. 104 (1988), 703-706
MSC: Primary 20E06; Secondary 20E26
MathSciNet review: 935110
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Abstract: It is shown that if at least two of the factor groups of a nontrivial amalgamated free product $ G$ satisfy nontrivial identities, then a special form of the profinite closure of the associated subgroups is necessary (as well as sufficient) for the residual finiteness of $ G$. An example shows that the necessity no longer holds if only one of the factor groups satisfies an identity.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0935110-8
PII: S 0002-9939(1988)0935110-8
Keywords: Residual finiteness, amalgamated free product, tree product, nontrivial identity on groups
Article copyright: © Copyright 1988 American Mathematical Society