Illinois Journal of Mathematics

Exponentially generic subsets of groups

Robert Gilman, Alexei Miasnikov, and Denis Osin

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Abstract

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.

Article information

Source
Illinois J. Math. Volume 54, Number 1 (2010), 371-388.

Dates
First available in Project Euclid: 9 March 2011

Permanent link to this document
http://projecteuclid.org/euclid.ijm/1299679753

Zentralblatt MATH identifier
05882261

Mathematical Reviews number (MathSciNet)
MR2777000

Subjects
Primary: 20F10: Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70]
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups 43A07: Means on groups, semigroups, etc.; amenable groups

Citation

Gilman, Robert; Miasnikov, Alexei; Osin, Denis. Exponentially generic subsets of groups. Illinois J. Math. 54 (2010), no. 1, 371--388. http://projecteuclid.org/euclid.ijm/1299679753.


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