Exponentially generic subsets of groups

Details Exponentially generic subsets of groups Exponentially generic subsets of groups

2010-07-04

arxiv.org/abs/1007.0552v1

Mathematics

Group Theory

17 pages, 1 figure

Scientific paper

In this paper we study the generic, i.e., typical, behavior of finitely generated subgroups of hyperbolic groups and also the generic behavior of the word problem for amenable groups. We show that a random set of elements of a nonelementary word hyperbolic group is very likely to be a set of free generators for a nicely embedded free subgroup. We also exhibit some finitely presented amenable groups for which the restriction of the word problem is unsolvable on every sufficiently large subset of words.

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