An improved diameter bound for finite simple groups of Lie type

Halasi, Z; Maróti, A; Pyber, L; Qiao, Y

An improved diameter bound for finite simple groups of Lie type

Halasi, Z Maróti, A Pyber, L Qiao, Y

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Publication Type:: Journal Article
Citation:: Bulletin of the London Mathematical Society, 2019, 51 (4), pp. 645 - 657
Issue Date:: 2019-08-01

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Field	Value	Language
dc.contributor.author	Halasi, Z	en_US
dc.contributor.author	Maróti, A	en_US
dc.contributor.author	Pyber, L	en_US
dc.contributor.author	Qiao, Y https://orcid.org/0000-0003-4334-1449	en_US
dc.date.issued	2019-08-01	en_US
dc.identifier.citation	Bulletin of the London Mathematical Society, 2019, 51 (4), pp. 645 - 657	en_US
dc.identifier.issn	0024-6093	en_US
dc.identifier.uri	http://hdl.handle.net/10453/137322
dc.description.abstract	© 2019 London Mathematical Society For a finite group (Formula presented.), let (Formula presented.) denote the maximum diameter of a connected Cayley graph of (Formula presented.). A well-known conjecture of Babai states that (Formula presented.) is bounded by (Formula presented.) in case (Formula presented.) is a non-abelian finite simple group. Let (Formula presented.) be a finite simple group of Lie type of Lie rank (Formula presented.) over the field (Formula presented.). Babai's conjecture has been verified in case (Formula presented.) is bounded, but it is wide open in case (Formula presented.) is unbounded. Recently, Biswas and Yang proved that (Formula presented.) is bounded by (Formula presented.). We show that in fact (Formula presented.) holds. Note that our bound is significantly smaller than the order of (Formula presented.) for (Formula presented.) large, even if (Formula presented.) is large. As an application, we show that more generally (Formula presented.) holds for any subgroup (Formula presented.) of (Formula presented.), where (Formula presented.) is a vector space of dimension (Formula presented.) defined over the field (Formula presented.).	en_US
dc.relation	http://purl.org/au-research/grants/arc/DE150100720
dc.relation.ispartof	Bulletin of the London Mathematical Society	en_US
dc.relation.isbasedon	10.1112/blms.12257	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.subject.classification	General Mathematics	en_US
dc.title	An improved diameter bound for finite simple groups of Lie type	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	51	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access	*
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	51	en_US

Abstract:

© 2019 London Mathematical Society For a finite group (Formula presented.), let (Formula presented.) denote the maximum diameter of a connected Cayley graph of (Formula presented.). A well-known conjecture of Babai states that (Formula presented.) is bounded by (Formula presented.) in case (Formula presented.) is a non-abelian finite simple group. Let (Formula presented.) be a finite simple group of Lie type of Lie rank (Formula presented.) over the field (Formula presented.). Babai's conjecture has been verified in case (Formula presented.) is bounded, but it is wide open in case (Formula presented.) is unbounded. Recently, Biswas and Yang proved that (Formula presented.) is bounded by (Formula presented.). We show that in fact (Formula presented.) holds. Note that our bound is significantly smaller than the order of (Formula presented.) for (Formula presented.) large, even if (Formula presented.) is large. As an application, we show that more generally (Formula presented.) holds for any subgroup (Formula presented.) of (Formula presented.), where (Formula presented.) is a vector space of dimension (Formula presented.) defined over the field (Formula presented.).

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http://hdl.handle.net/10453/137322