An explicit upper bound for the Helfgott delta in SL(2,p)

Jack Button, Colva Roney-Dougal

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
6 Downloads (Pure)


Helfgott proved that there exists a δ>0 such that if S is a symmetric generating subset of SL(2,p) containing 1 then either S3=SL(2,p) or |S3| ≥|S|1+δ. It is known that δ ≥ 1/3024. Here we show that δ ≤(log2(7)-1)/6 ≈ 0.3012 and we present evidence suggesting that this might be the true value of δ.

Original languageEnglish
Pages (from-to)493-511
Number of pages19
JournalJournal of Algebra
Early online date23 Sept 2014
Publication statusPublished - 1 Jan 2015


  • Simple group
  • Subset growth
  • Approximate subgroup


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