On the isolated points in the space of groups

Details On the isolated points in the space of groups On the isolated points in the space of groups

2005-11-29

arxiv.org/abs/math/0511714v2

J. Algebra 307(1) (2007), 254-277

Mathematics

Group Theory

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

Scientific paper

10.1016/j.jalgebra.2006.02.012

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.

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