New growth bounds for set products in the Heisenberg and affine groups over prime fields, plus an application to Freiman's isomorphism in nonabelian groups.
Collinear triples and quadruples for Cartesian products in $\mathbb{F}_p^2$
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abstract
In this ote, which has been absorbed by arXiv1702.01003, we combine a recent point-line incidence bound of Stevens and de Zeeuw with an older lemma of Bourgain, Katz and Tao to bound the number of collinear triples and quadruples in a Cartesian product in $\mathbb{F}_p^2$.
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2019 1verdicts
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Some remarks on products of sets in the Heisenberg group and in the affine group
New growth bounds for set products in the Heisenberg and affine groups over prime fields, plus an application to Freiman's isomorphism in nonabelian groups.