author/title/abstract/status

Authors: Antonio Diaz, Adam Glesser, Nadia Mazza, Sejong Park
Title: Glauberman and Thompson's theorems for fusion systems
Abstract: We prove analogues of results of Glauberman and Thompson for fusion
systems. Namely, given a (saturated) fusion system F on a finite
p-group S, and in the cases where p is odd or F is
S_4-free, we show that Z(N_F(J(S)))=Z(F) (Glauberman),
and that if C_F(Z(S))=N_F(J(S))=F_S(S), then
F=F_S(S) (Thompson). As a corollary, we obtain a stronger form
of Frobenius' theorem for fusion systems, applicable under the above
assumptions, and generalizing another result of Thompson.