Rank of matrices with entries from a multiplicative group
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math.NT
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rankmultiplicativeboundsentriesgroupgroupsmatricessmall
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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.
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