JournalsjemsVol. 13, No. 2pp. 331–343

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

  • Mark V. Sapir

    Vanderbilt University, Nashville, United States
  • Iva Špakulová

    Vanderbilt University, Nashville, USA
Almost all one-relator groups with at least three generators are residually finite cover
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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.

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. 331–343

DOI 10.4171/JEMS/255