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Abstract We establish lower bounds on the rank of matrices in which all but the diagonal entries lie in a multiplicative group of small rank. Applying these bounds we show that the distance sets of finite pointsets in $$\mathbb {R}^d$$ generate high-rank multiplicative groups and that multiplicative groups of small rank cannot contain large sumsets.more » « less
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Alon, Noga; Ruzsa, Imre; Solymosi, József (, Publicacions Matemàtiques)
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