On the isolated points in the space of groups

Yves de Cornulier; Luc Guyot; Wolfgang Pitsch

doi:10.1016/j.jalgebra.2006.02.012

On the isolated points in the space of groups

Yves de Cornulier, Luc Guyot, Wolfgang Pitsch

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

31 Citations (Scopus)

Abstract

We investigate the isolated points in the space of finitely generated groups. We give a workable characterization of isolated groups and study their hereditary properties. Various examples of groups are shown to yield isolated groups. We also discuss a connection between isolated groups and solvability of the word problem. © 2006 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	254-277
Journal	Journal of Algebra
Volume	307
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2006.02.012
Publication status	Published - 1 Jan 2007

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10.1016/j.jalgebra.2006.02.012

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AB - We investigate the isolated points in the space of finitely generated groups. We give a workable characterization of isolated groups and study their hereditary properties. Various examples of groups are shown to yield isolated groups. We also discuss a connection between isolated groups and solvability of the word problem. © 2006 Elsevier Inc. All rights reserved.

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JF - Journal of Algebra

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On the isolated points in the space of groups

Abstract

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