Simple fusion systems and the Solomon 2-local groups

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. (c) 2005 Elsevier Inc. All rights reserved.