Normal subsystems of fusion systems

In this article, we prove that, for any saturated fusion system, the (unique) smallest weakly normal subsystem of it on a given strongly closed subgroup is actually normal. This has a variety of corollaries, such as the statement that the notion of a simple fusion system is independent of whether on...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the London Mathematical Society 2011-08, Vol.84 (1), p.137-158
Main Author: Craven, David A.
Format: Article
Language:English
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c3067-ad60268115902dc74c3d9bf60ebba4a81d55b7119fa5cd3cacbbc5ba5f4c4313
cites
container_end_page 158
container_issue 1
container_start_page 137
container_title Journal of the London Mathematical Society
container_volume 84
creator Craven, David A.
description In this article, we prove that, for any saturated fusion system, the (unique) smallest weakly normal subsystem of it on a given strongly closed subgroup is actually normal. This has a variety of corollaries, such as the statement that the notion of a simple fusion system is independent of whether one uses weakly normal or normal subsystems. We also develop a theory of weakly normal maps, consider intersections and products of weakly normal subsystems, and the hypercentre of a fusion system.
doi_str_mv 10.1112/jlms/jdr004
format article
fullrecord <record><control><sourceid>oup_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1112_jlms_jdr004</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><oup_id>10.1112/jlms/jdr004</oup_id><sourcerecordid>10.1112/jlms/jdr004</sourcerecordid><originalsourceid>FETCH-LOGICAL-c3067-ad60268115902dc74c3d9bf60ebba4a81d55b7119fa5cd3cacbbc5ba5f4c4313</originalsourceid><addsrcrecordid>eNp9j81Kw0AYRQdRMFZXvkBAcCOx35f5a5ZSrFpSXdj9MD8ZSEhMmTFI3t6UdN3Vhcu5Fw4h9wjPiJgvm7aLy8YFAHZBEmSiyKTkcEkSgJxlAkFek5sYGwCkCHlCHj770Ok2jYOJY_ytupj2PvVDrPuf9NTckiuv21jdnXJB9pvX_fo9K7_ePtYvZWYpCJlpJyAXK0ReQO6sZJa6wngBlTGa6RU6zo1ELLzm1lGrrTGWG809s4wiXZCn-daGPsZQeXUIdafDqBDUUU8d9dSsN9E40391W43nULUtd9-Tr5w2j_OmHw5nz_8BHVZhqw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Normal subsystems of fusion systems</title><source>Wiley-Blackwell Read &amp; Publish Collection</source><creator>Craven, David A.</creator><creatorcontrib>Craven, David A.</creatorcontrib><description>In this article, we prove that, for any saturated fusion system, the (unique) smallest weakly normal subsystem of it on a given strongly closed subgroup is actually normal. This has a variety of corollaries, such as the statement that the notion of a simple fusion system is independent of whether one uses weakly normal or normal subsystems. We also develop a theory of weakly normal maps, consider intersections and products of weakly normal subsystems, and the hypercentre of a fusion system.</description><identifier>ISSN: 0024-6107</identifier><identifier>EISSN: 1469-7750</identifier><identifier>DOI: 10.1112/jlms/jdr004</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>Journal of the London Mathematical Society, 2011-08, Vol.84 (1), p.137-158</ispartof><rights>2011 London Mathematical Society 2011</rights><rights>2011 London Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3067-ad60268115902dc74c3d9bf60ebba4a81d55b7119fa5cd3cacbbc5ba5f4c4313</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Craven, David A.</creatorcontrib><title>Normal subsystems of fusion systems</title><title>Journal of the London Mathematical Society</title><description>In this article, we prove that, for any saturated fusion system, the (unique) smallest weakly normal subsystem of it on a given strongly closed subgroup is actually normal. This has a variety of corollaries, such as the statement that the notion of a simple fusion system is independent of whether one uses weakly normal or normal subsystems. We also develop a theory of weakly normal maps, consider intersections and products of weakly normal subsystems, and the hypercentre of a fusion system.</description><issn>0024-6107</issn><issn>1469-7750</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9j81Kw0AYRQdRMFZXvkBAcCOx35f5a5ZSrFpSXdj9MD8ZSEhMmTFI3t6UdN3Vhcu5Fw4h9wjPiJgvm7aLy8YFAHZBEmSiyKTkcEkSgJxlAkFek5sYGwCkCHlCHj770Ok2jYOJY_ytupj2PvVDrPuf9NTckiuv21jdnXJB9pvX_fo9K7_ePtYvZWYpCJlpJyAXK0ReQO6sZJa6wngBlTGa6RU6zo1ELLzm1lGrrTGWG809s4wiXZCn-daGPsZQeXUIdafDqBDUUU8d9dSsN9E40391W43nULUtd9-Tr5w2j_OmHw5nz_8BHVZhqw</recordid><startdate>201108</startdate><enddate>201108</enddate><creator>Craven, David A.</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>201108</creationdate><title>Normal subsystems of fusion systems</title><author>Craven, David A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3067-ad60268115902dc74c3d9bf60ebba4a81d55b7119fa5cd3cacbbc5ba5f4c4313</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Craven, David A.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of the London Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Craven, David A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Normal subsystems of fusion systems</atitle><jtitle>Journal of the London Mathematical Society</jtitle><date>2011-08</date><risdate>2011</risdate><volume>84</volume><issue>1</issue><spage>137</spage><epage>158</epage><pages>137-158</pages><issn>0024-6107</issn><eissn>1469-7750</eissn><abstract>In this article, we prove that, for any saturated fusion system, the (unique) smallest weakly normal subsystem of it on a given strongly closed subgroup is actually normal. This has a variety of corollaries, such as the statement that the notion of a simple fusion system is independent of whether one uses weakly normal or normal subsystems. We also develop a theory of weakly normal maps, consider intersections and products of weakly normal subsystems, and the hypercentre of a fusion system.</abstract><pub>Oxford University Press</pub><doi>10.1112/jlms/jdr004</doi><tpages>22</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0024-6107
ispartof Journal of the London Mathematical Society, 2011-08, Vol.84 (1), p.137-158
issn 0024-6107
1469-7750
language eng
recordid cdi_crossref_primary_10_1112_jlms_jdr004
source Wiley-Blackwell Read & Publish Collection
title Normal subsystems of fusion systems
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T20%3A17%3A23IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-oup_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Normal%20subsystems%20of%20fusion%20systems&rft.jtitle=Journal%20of%20the%20London%20Mathematical%20Society&rft.au=Craven,%20David%20A.&rft.date=2011-08&rft.volume=84&rft.issue=1&rft.spage=137&rft.epage=158&rft.pages=137-158&rft.issn=0024-6107&rft.eissn=1469-7750&rft_id=info:doi/10.1112/jlms/jdr004&rft_dat=%3Coup_cross%3E10.1112/jlms/jdr004%3C/oup_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c3067-ad60268115902dc74c3d9bf60ebba4a81d55b7119fa5cd3cacbbc5ba5f4c4313%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_oup_id=10.1112/jlms/jdr004&rfr_iscdi=true