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Reduced fusion systems over 2-groups of small order

Andersen, Kasper K.S. LU ; Oliver, Bob and Ventura, Joana (2017) In Journal of Algebra 489. p.310-372
Abstract

We prove, when S is a 2-group of order at most 29, that each reduced fusion system over S is the fusion system of a finite simple group and is tame. It then follows that each saturated fusion system over a 2-group of order at most 29 is realizable. What is most interesting about this result is the method of proof: we show that among 2-groups with order in this range, the ones which can be Sylow 2-subgroups of finite simple groups are almost completely determined by criteria based on Bender's classification of groups with strongly 2-embedded subgroups.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Finite simple groups, Fusion, Sylow subgroups
in
Journal of Algebra
volume
489
pages
63 pages
publisher
Elsevier
external identifiers
  • scopus:85024492596
ISSN
0021-8693
DOI
10.1016/j.jalgebra.2017.06.016
language
English
LU publication?
yes
id
67a3dd05-fab6-4565-aa61-6a8ee57fc61c
date added to LUP
2017-07-31 08:20:05
date last changed
2017-07-31 08:20:05
@article{67a3dd05-fab6-4565-aa61-6a8ee57fc61c,
  abstract     = {<p>We prove, when S is a 2-group of order at most 2<sup>9</sup>, that each reduced fusion system over S is the fusion system of a finite simple group and is tame. It then follows that each saturated fusion system over a 2-group of order at most 2<sup>9</sup> is realizable. What is most interesting about this result is the method of proof: we show that among 2-groups with order in this range, the ones which can be Sylow 2-subgroups of finite simple groups are almost completely determined by criteria based on Bender's classification of groups with strongly 2-embedded subgroups.</p>},
  author       = {Andersen, Kasper K.S. and Oliver, Bob and Ventura, Joana},
  issn         = {0021-8693},
  keyword      = {Finite simple groups,Fusion,Sylow subgroups},
  language     = {eng},
  month        = {11},
  pages        = {310--372},
  publisher    = {Elsevier},
  series       = {Journal of Algebra},
  title        = {Reduced fusion systems over 2-groups of small order},
  url          = {http://dx.doi.org/10.1016/j.jalgebra.2017.06.016},
  volume       = {489},
  year         = {2017},
}