A characterization of the 2-fusion system of L_4(q)

Bibliographic Details
Main Author:	Lynd, Justin
Language:	English
Published:	The Ohio State University / OhioLINK 2012
Subjects:	Mathematics fusion system p-local finite group classification of finite simple groups
Online Access:	http://rave.ohiolink.edu/etdc/view?acc_num=osu1337790920

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spelling	ndltd-OhioLink-oai-etd.ohiolink.edu-osu13377909202021-08-03T06:05:02Z A characterization of the 2-fusion system of L_4(q) Lynd, Justin Mathematics fusion system p-local finite group classification of finite simple groups We study saturated fusion systems F on a finite 2-group S with an involution centralizer having a unique component on a dihedral group and containing the Baumann subgroup of S. Assuming F is perfect with no nontrivial normal 2-subgroups and the centralizer of the component is a cyclic 2-group, it is shown F is uniquely determined as the 2-fusion system of L_4(q) for some q = 3 (mod 4). This should be viewed as a contribution to a program recently outlined by Aschbacher for the classification of simple fusion systems at the prime 2. The analogous problem in the classification of finite simple groups of component type (the L_2(q), A_7 standard component problem) was one of the last to be completed, and was ultimately only resolved in an inductive context with heavy machinery. Thanks primarily to the hypothesis concerning the Baumann subgroup and the absence of cores, our arguments by contrast require only 2-fusion analysis and transfer. We prove a generalization of the Thompson transfer lemma in the context of fusion systems, which is applied often. 2012-06-22 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1337790920 http://rave.ohiolink.edu/etdc/view?acc_num=osu1337790920 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection	NDLTD
language	English
sources	NDLTD
topic	Mathematics fusion system p-local finite group classification of finite simple groups
spellingShingle	Mathematics fusion system p-local finite group classification of finite simple groups Lynd, Justin A characterization of the 2-fusion system of L_4(q)
author	Lynd, Justin
author_facet	Lynd, Justin
author_sort	Lynd, Justin
title	A characterization of the 2-fusion system of L_4(q)
title_short	A characterization of the 2-fusion system of L_4(q)
title_full	A characterization of the 2-fusion system of L_4(q)
title_fullStr	A characterization of the 2-fusion system of L_4(q)
title_full_unstemmed	A characterization of the 2-fusion system of L_4(q)
title_sort	characterization of the 2-fusion system of l_4(q)
publisher	The Ohio State University / OhioLINK
publishDate	2012
url	http://rave.ohiolink.edu/etdc/view?acc_num=osu1337790920
work_keys_str_mv	AT lyndjustin acharacterizationofthe2fusionsystemofl4q AT lyndjustin characterizationofthe2fusionsystemofl4q
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A characterization of the 2-fusion system of L_4(q)

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