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FusionSystems TERMINATED

Simple fusion systems and linking systems

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EC-Contrib. €

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Project "FusionSystems" data sheet

The following table provides information about the project.

Coordinator
THE UNIVERSITY COURT OF THE UNIVERSITY OF ABERDEEN 

Organization address
address: KING'S COLLEGE REGENT WALK
city: ABERDEEN
postcode: AB24 3FX
website: http://www.abdn.ac.uk

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country United Kingdom [UK]
 Project website https://www.abdn.ac.uk/ncs/departments/mathematics/
 Total cost 195˙454 €
 EC max contribution 195˙454 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2015
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2016
 Duration (year-month-day) from 2016-08-01   to  2018-07-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE UNIVERSITY COURT OF THE UNIVERSITY OF ABERDEEN UK (ABERDEEN) coordinator 195˙454.00

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 Project objective

The classification of finite simple groups is often regarded as one of the major mathematical achievements of the 20th century. Its importance lies not only in the fundamental result, but also in the methodology and conceptual framework developed for its proof. Most intriguingly, it turned out that the structure of a finite group is closely connected to the structure of the p-local subgroups, i.e. the normalizers of non-trivial p-subgroups, for a suitably chosen prime p. Of particular importance is the prime 2. Even though the proof of the classification of finite simple groups is insightful in its major conceptual approach, it is extremely long and difficult in its details. Thus, it would be of great interest to obtain a simplified proof. Moreover, to gain the maximum benefit from the methods of the proof of the classification, it is highly desirable to work in a more general context which in particular allows also for applications in the modular representation theory of finite groups. Saturated fusion systems provide a conceptual framework for this and connect to important questions in homotopy theory. A program to find a new and better proof of the classification of finite simple groups through a classification of simple fusion systems at the prime 2 has been recently outlined by Aschbacher. Two parts of our proposal concern classification problems for fusion systems. Their significance lies not only in completing important cases in Aschbacher's program, but also in giving new insight into the relative abundance of exotic examples, i.e. fusion systems not induced by any finite group. In the third part we attack a major problem in the algebraic theory of fusion systems by defining an analogue in fusion systems of centralizers of subgroups of finite groups. This will simultaneously facilitate a classification of fusion systems in the spirit of Aschbacher's program, and lead to a combinatorial understanding of maps between classifying spaces of fusion systems.

 Publications

year authors and title journal last update
List of publications.
2017 Ellen Henke and Justin Lynd
Subintrinsic Benson-Solomon components
published pages: , ISSN: , DOI:
2019-06-13
2017 Ellen Henke and Justin Lynd
Extensions of the Benson-Solomon fusion systems
published pages: , ISSN: , DOI:
2019-06-13
2017 Justin Lynd and Jason Semeraro
On the number of simple modules of a Benson-Solomon fusion system
published pages: , ISSN: , DOI:
2019-06-13

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