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Quasirandom groups

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arxiv 0710.3877 v1 pith:TR5HEYRM submitted 2007-10-20 math.CO math.GR

W. T. Gowers This is my paper · ORCID
classification math.COmath.GR
keywords subsetgroupproduct-freeansweraskedbabaiconditionconstant
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Babai and S\'os have asked whether there exists a constant c>0 such that every finite group G has a product-free subset of size at least c|G|: that is, a subset X that does not contain three elements x, y and z with xy=z. In this paper we show that the answer is no. Moreover, we give a simple sufficient condition for a group not to have any large product-free subset.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A General Framework for Low Soundness Homomorphism Testing

    cs.CC 2025-09 reject novelty 7.0 of 10

    A moment identity over homomorphisms yields candidate low-soundness tests for cyclic, automorphism, and Lie settings, but one headline theorem is stated with an impossible guarantee.

  2. Representation gaps of rigid planar diagram monoids

    math.RT 2025-05 conditional novelty 6.0 of 10

    Rigid non-pivotal Temperley-Lieb, Motzkin, and planar rook monoids have smaller representation gaps than their pivotal counterparts, making them worse for cryptographic use.

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