Let G be a group and \Gamma a G-invariant set of nilpotent subgroups of G. Suppose that \Gamma fulfills the maximum and minimum condition and that for all P,Q in \Gamma, both P\cap Q and NP(Q) N Q(P) are in Gamma. Then \Gamma is called a nilpotent subgroup system(NSS). Our main theorem is a generalization of Glauberman's characterization of the natural SL2-module from finite groups to groups with an NSS.
Last Revised 06/10/2002