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

Jack Button; Colva Roney-Dougal

doi:10.1016/j.jalgebra.2014.09.001

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

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	493-511
Number of pages	19
Journal	Journal of Algebra
Volume	421
Early online date	23 Sept 2014
DOIs	https://doi.org/10.1016/j.jalgebra.2014.09.001
Publication status	Published - 1 Jan 2015

Keywords

Simple group
Subset growth
Approximate subgroup

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10.1016/j.jalgebra.2014.09.001

button2015jalgebra493
Copyright © 2014 Published by Elsevier Inc. This is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Algebra 421, 493-511, 1 January 2015 DOI https://doi.org/10.1016/j.jalgebra.2014.09.001
Accepted author manuscript, 220 KB

Solving word problems: Solving word problems via generalisations of small cancellation
Roney-Dougal, C. (PI) & Neunhoeffer, M. (CoI)
EPSRC
1/10/11 → 30/09/14
Project: Standard

Colva Roney-Dougal, OBE
- Colva.Roney-Dougalst-andrews.acuk
Person: Academic

Cite this

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AB - 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.

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KW - Subset growth

KW - Approximate subgroup

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

Abstract

Keywords

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Solving word problems: Solving word problems via generalisations of small cancellation

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Colva Roney-Dougal, OBE

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