Reduced fusion systems over 2-groups of small order
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/67a3dd05-fab6-4565-aa61-6a8ee57fc61c
- author
- Andersen, Kasper K.S.
LU
; Oliver, Bob and Ventura, Joana
- organization
- publishing date
- 2017-11-01
- 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
- 2022-04-25 01:38:40
@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}}, keywords = {{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}}, doi = {{10.1016/j.jalgebra.2017.06.016}}, volume = {{489}}, year = {{2017}}, }