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Simple fusion systems and the Solomon 2-local groups

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
296
Issue
2
Identifiers
DOI: 10.1016/j.jalgebra.2005.09.024

Abstract

Abstract We introduce a notion of simple fusion systems which imitates the corresponding notion for finite groups and show that the fusion system on the Sylow-2-subgroup of a 7-dimensional spinor group over a field of characteristic 3 considered by Ron Solomon [R. Solomon, Finite groups with Sylow-2-subgroups of type 3, J. Algebra 28 (1974) 182–198] and by Ran Levi and Bob Oliver [R. Levi, R. Oliver, Construction of 2-local finite groups of a type studied by Solomon and Benson, Geom. Topol. 6 (2002) 917–990] is simple in this sense.

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