ZJ-theorems for fusion systems

Kessar, R. & Linckelmann, M. (2008). ZJ-theorems for fusion systems. Transactions of the American Mathematical Society, 360(6), pp. 3093-3106. doi: 10.1090/S0002-9947-08-04275-X

Abstract

For p an odd prime, we generalise the Glauberman-Thompson p-nilpotency theorem [5, Ch. 8, Theorem 3.1] to arbitrary fusion systems. We define a notion of Qd(p)- free fusion systems and show that if F is a Qd(p)-free fusion system on some finite p-group P then F is controlled by W(P) for any Glauberman functor W, generalising Glauberman’s ZJ-theorem [3] to arbitrary fusion systems.