On the isolated points in the space of groups

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.

30 pages, no figure. v2: minor changes, published version from March 2006

References in corpus (3)

• Limit groups as limits of free groups: compactifying the set of free groups
• Finitely presented wreath products and double coset decompositions
• Finitely presentable, non-Hopfian groups with Kazhdan's Property (T) and infinite outer automorphism group

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