Open Access
Spring 2010 Exponentially generic subsets of groups
Robert Gilman, Alexei Miasnikov, Denis Osin
Illinois J. Math. 54(1): 371-388 (Spring 2010). DOI: 10.1215/ijm/1299679753

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.

Citation

Download Citation

Robert Gilman. Alexei Miasnikov. Denis Osin. "Exponentially generic subsets of groups." Illinois J. Math. 54 (1) 371 - 388, Spring 2010. https://doi.org/10.1215/ijm/1299679753

Information

Published: Spring 2010
First available in Project Euclid: 9 March 2011

zbMATH: 1243.20045
MathSciNet: MR2777000
Digital Object Identifier: 10.1215/ijm/1299679753

Subjects:
Primary: 20F10
Secondary: 20F67 , ‎43A07‎

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

Vol.54 • No. 1 • Spring 2010
Back to Top