TY - JOUR
T1 - Exponentially generic subsets of groups
AU - Gilman, Robert
AU - Miasnikov, Alexei
AU - Osin, Denis
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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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U2 - 10.1215/ijm/1299679753
DO - 10.1215/ijm/1299679753
M3 - Article
AN - SCOPUS:79955953275
SN - 0019-2082
VL - 54
SP - 371
EP - 388
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
IS - 1
ER -