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

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 2, page 331-343
- ISSN: 1435-9855

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topSapir, 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 -

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