IMAGES OF GOLOD-SHAFAREVICH ALGEBRAS WITH SMALL GROWTH

Agata Smoktunowicz, Laurent Bartholdi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We show that Golod-Shafarevich algebras can be homomorphically mapped onto infinite dimensional algebras with polynomial growth when mild assumptions about the number of relations of given degrees are introduced. This answers a question by Zel'manov. In the case where these algebras are finitely presented, we show that they can be mapped onto infinite-dimensional algebras with at most quadratic growth. We then use an elementary construction to show that any sufficiently regular function a parts per thousand(3) n(log n) may occur as the growth function of an algebra.

Original languageEnglish
Pages (from-to)421-438
Number of pages18
JournalQuarterly Journal of Mathematics
Volume65
Issue number2
Early online date28 Mar 2013
DOIs
Publication statusPublished - 1 Jun 2014

Keywords

  • DIMENSION

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