Year: 2010
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Gilman, Robert, Miasnikov, Alexei, Osin, Denis
Institutions: Stevens Institute of Technology, Vanderbilt University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951300958