An uncountable family of finitely generated residually finite groups

Author:

Chong Hip Kuen1,Wise Daniel T.1

Affiliation:

1. Department of Mathematics & Statistics , McGill University , Montreal , QC H3A 0B9 , Canada

Abstract

Abstract We study a family of finitely generated residually finite groups. These groups are doubles F 2 * H F 2 F_{2}*_{H}F_{2} of a rank-2 free group F 2 F_{2} along an infinitely generated subgroup 𝐻. Varying 𝐻 yields uncountably many groups up to isomorphism.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference17 articles.

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3. V. H. Dyson, The word problem and residuallly finite groups, Notices Amer. Math. Soc. 11 (1964), Paper No. 743.

4. V. H. Dyson, A family of groups with nice word problems, J. Aust. Math. Soc. 17 (1974), 414–425.

5. R. I. Grigorchuk, Degrees of growth of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984), no. 5, 939–985.

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