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

Mark V. Sapir, Iva Špakulová (2011)

Journal of the European Mathematical Society

We prove that with probability tending to 1, a one-relator group with at least three generators and the relator of length is residually finite, is a virtually residually (finite -)group for all sufficiently large , and is coherent. The proof uses both combinatorial group theory and non-trivial results about Brownian motions.

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