Exponentially generic subsets of groups

Robert Gilman, Alexei Miasnikov, Denis Osin

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

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.

Original languageEnglish
Pages (from-to)371-388
Number of pages18
JournalIllinois Journal of Mathematics
Volume54
Issue number1
DOIs
StatePublished - 2010

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