JournalspmVol. 68 / No. 2DOI 10.4171/pm/1888

Bi-Lipschitz equivalent metrics on groups, and a problem in additive number theory

  • Melvyn B. Nathanson

    Lehman College, CUNY, Bronx, USA
Bi-Lipschitz equivalent metrics on groups, and a problem in additive number theory cover

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Abstract

There is a standard “word length” metric canonically associated to any set of generators for a group. In particular, for any integers and greater than , the additive group has generating sets and with associated metrics and , respectively. It is proved that these metrics are bi-Lipschitz equivalent if and only if there exist positive integers and such that .