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

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

2008-09-26

arxiv.org/abs/0809.4693v2

Mathematics

Group Theory

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

Scientific paper

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.

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