English

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

Group Theory 2009-09-13 v2 Probability

Abstract

We prove that with probability tending to 1, a 1-relator group with at least 3 generators and relator of length n is residually finite, virtually residually (finite p)-group for all sufficiently large p, and coherent. The proof uses both combinatorial group theory and non-trivial results about Brownian motions, bridges and excursions in R^k.

Keywords

Cite

@article{arxiv.0809.4693,
  title  = {Almost all one-relator groups with at least three generators are residually finite},
  author = {Mark Sapir and Iva Spakulova},
  journal= {arXiv preprint arXiv:0809.4693},
  year   = {2009}
}

Comments

11 pages. Comments are welcome. v2: Added a new probabilistic model: counting 1-relataed groups up o isomorphism, not words as before

R2 v1 2026-06-21T11:24:41.001Z