Rank of Matrices with Entries from a Multiplicative Group

Noga Alon, József Solymosi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 generate high-rank multiplicative groups and that multiplicative groups of small rank cannot contain large sumsets.

Original languageEnglish
Pages (from-to)12383-12399
Number of pages17
JournalInternational Mathematics Research Notices
Issue number14
StatePublished - 1 Jul 2023


FundersFunder number
Hungarian National ResearchKKP 133819
National Science FoundationDMS-1855464
Natural Sciences and Engineering Research Council of Canada
United States-Israel Binational Science Foundation2018267
Hungarian Scientific Research FundK 119528


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