REDUCTIONS TO SIMPLE FUSION SYSTEMS

Bob Oliver (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We prove that if E F are saturated fusion systems over p-groups T S, such that C S (E) ≤ T , and either Aut F (T)/Aut E (T) or Out(E) is p-solvable, then F can be " reduced " to E by alternately taking normal subsystems of p-power index or of index prime to p. In particular, this is the case whenever E is simple and " tamely realized " by a known simple group K. This answers a question posed by Michael Aschbacher, and is useful when analyzing involution centralizers in simple fusion systems, in connection with his program for reproving parts of the classification of finite simple groups by classifying certain 2-fusion systems.

Mots clés: Fusion systems; Sylow subgroups; finite simple groups; generalized Fitting subgroup; p-solvable groups

Domaines: Théorie des groupes [math.GR]

Bob Oliver. REDUCTIONS TO SIMPLE FUSION SYSTEMS. Bulletin of London Mathematical Society, 2016. ⟨hal-01340088⟩