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

Button, Jack; Roney-Dougal, Colva

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dc.contributor.author	Button, Jack
dc.contributor.author	Roney-Dougal, Colva
dc.date.accessioned	2014-11-20T16:31:02Z
dc.date.available	2014-11-20T16:31:02Z
dc.date.issued	2015-01-01
dc.identifier.citation	Button , J & Roney-Dougal , C 2015 , ' An explicit upper bound for the Helfgott delta in SL(2,p) ' , Journal of Algebra , vol. 421 , pp. 493-511 . https://doi.org/10.1016/j.jalgebra.2014.09.001	en
dc.identifier.issn	0021-8693
dc.identifier.other	PURE: 157245877
dc.identifier.other	PURE UUID: 9bdb89a6-8ae2-4f7a-addf-4fe7530ba593
dc.identifier.other	ArXiv: http://arxiv.org/abs/1401.2863v1
dc.identifier.other	Scopus: 84908568382
dc.identifier.other	WOS: 000345194400025
dc.identifier.other	ORCID: /0000-0002-0532-3349/work/73700936
dc.identifier.uri	https://hdl.handle.net/10023/5819
dc.description.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.
dc.format.extent	19
dc.language.iso	eng
dc.relation.ispartof	Journal of Algebra	en
dc.rights	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	en
dc.subject	Simple group	en
dc.subject	Subset growth	en
dc.subject	Approximate subgroup	en
dc.subject	QA Mathematics	en
dc.subject	T-NDAS	en
dc.subject	BDC	en
dc.subject.lcc	QA	en
dc.title	An explicit upper bound for the Helfgott delta in SL(2,p)	en
dc.type	Journal article	en
dc.contributor.sponsor	EPSRC	en
dc.description.version	Postprint	en
dc.contributor.institution	University of St Andrews. Pure Mathematics	en
dc.contributor.institution	University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra	en
dc.identifier.doi	https://doi.org/10.1016/j.jalgebra.2014.09.001
dc.description.status	Peer reviewed	en
dc.date.embargoedUntil	2016-01-01
dc.identifier.grantnumber	EP/I03582X/1	en

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