Almost all one-relator groups with at least three generators are residually finite

Sapir, Mark V., and Špakulová, Iva. "Almost all one-relator groups with at least three generators are residually finite." Journal of the European Mathematical Society 013.2 (2011): 331-343. <http://eudml.org/doc/277370>.

@article{Sapir2011,
abstract = {We prove that with probability tending to 1, a one-relator group with at least three generators and the relator of length $n$ is residually finite, is a virtually residually (finite $p$-)group for all sufficiently large $p$, and is coherent. The proof uses both combinatorial group theory and non-trivial results about Brownian motions.},
author = {Sapir, Mark V., Špakulová, Iva},
journal = {Journal of the European Mathematical Society},
keywords = {one-relator group; residually finite; coherent; Brownian motion; random groups; ascending HNN extensions; finitely generated subgroups; one-relator groups; residually finite groups; random groups; ascending HNN extensions; finitely generated subgroups},
language = {eng},
number = {2},
pages = {331-343},
publisher = {European Mathematical Society Publishing House},
title = {Almost all one-relator groups with at least three generators are residually finite},
url = {http://eudml.org/doc/277370},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Sapir, Mark V.
AU - Špakulová, Iva
TI - Almost all one-relator groups with at least three generators are residually finite
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 2
SP - 331
EP - 343
AB - We prove that with probability tending to 1, a one-relator group with at least three generators and the relator of length $n$ is residually finite, is a virtually residually (finite $p$-)group for all sufficiently large $p$, and is coherent. The proof uses both combinatorial group theory and non-trivial results about Brownian motions.
LA - eng
KW - one-relator group; residually finite; coherent; Brownian motion; random groups; ascending HNN extensions; finitely generated subgroups; one-relator groups; residually finite groups; random groups; ascending HNN extensions; finitely generated subgroups
UR - http://eudml.org/doc/277370
ER -