CLASSIFICATION OF REFLECTION SUBGROUPS MINIMALLY CONTAINING p-SYLOW SUBGROUPS

Townsend, KD

CLASSIFICATION OF REFLECTION SUBGROUPS MINIMALLY CONTAINING p-SYLOW SUBGROUPS

Townsend, KD

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Publisher:: Cambridge University Press
Publication Type:: Journal Article
Citation:: Bulletin of the Australian Mathematical Society, 2018, 97, (1), pp. 57-68
Issue Date:: 2018-02-01

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Field	Value	Language
dc.contributor.author	Townsend, KD
dc.date.accessioned	2022-09-08T20:42:00Z
dc.date.available	2022-09-08T20:42:00Z
dc.date.issued	2018-02-01
dc.identifier.citation	Bulletin of the Australian Mathematical Society, 2018, 97, (1), pp. 57-68
dc.identifier.issn	0004-9727
dc.identifier.issn	1755-1633
dc.identifier.uri	http://hdl.handle.net/10453/161558
dc.description.abstract	Let a prime p divide the order of a finite real reflection group. We classify the reflection subgroups up to conjugacy that are minimal with respect to inclusion, subject to containing a p -Sylow subgroup. For Weyl groups, this is achieved by an algorithm inspired by the Borel–de Siebenthal algorithm. The cases where there is not a unique conjugacy class of reflection subgroups minimally containing the p -Sylow subgroups are the groups of type F4 when p=2 and I2(m) when m≥6 is even but not a power of 2 for each odd prime divisor p of m . The classification significantly reduces the cases required to describe the p -Sylow subgroups of finite real reflection groups.
dc.language	English
dc.publisher	Cambridge University Press
dc.relation.ispartof	Bulletin of the Australian Mathematical Society
dc.relation.isbasedon	10.1017/S0004972717000764
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0101 Pure Mathematics
dc.subject.classification	General Mathematics
dc.title	CLASSIFICATION OF REFLECTION SUBGROUPS MINIMALLY CONTAINING p-SYLOW SUBGROUPS
dc.type	Journal Article
utslib.citation.volume	97
utslib.for	0101 Pure Mathematics
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access	*
pubs.consider-herdc	false
dc.date.updated	2022-09-08T20:41:58Z
pubs.issue	1
pubs.publication-status	Published
pubs.volume	97
utslib.citation.issue	1

Abstract:

Let a prime p divide the order of a finite real reflection group. We classify the reflection subgroups up to conjugacy that are minimal with respect to inclusion, subject to containing a p -Sylow subgroup. For Weyl groups, this is achieved by an algorithm inspired by the Borel–de Siebenthal algorithm. The cases where there is not a unique conjugacy class of reflection subgroups minimally containing the p -Sylow subgroups are the groups of type F4 when p=2 and I2(m) when m≥6 is even but not a power of 2 for each odd prime divisor p of m . The classification significantly reduces the cases required to describe the p -Sylow subgroups of finite real reflection groups.

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http://hdl.handle.net/10453/161558