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.
Cite this article
Mark V. Sapir, Iva Špakulová, Almost all one-relator groups with at least three generators are residually finite. J. Eur. Math. Soc. 13 (2011), no. 2, pp. 331–343DOI 10.4171/JEMS/255