nLab
generalized Fitting subgroup

One definition of the generalized Fitting subgroup F *(G)F^*(G) of a group GG is that it is the subgroup generated by all normal subgroups NN of GG possessing subgroups N 1,N 2,,N rN_1,N_2,\dots, N_r for some integer rr such that N=N 1N 2N rN=N_1N_2\cdots N_r; x ix j=x jx ix_i x_j=x_j x_i for all x iN ix_i\in N_i, x jN jx_j\in N_j, and distinct subscripts ii and jj; and each N iN_i either has prime power order or is a quasisimple group. Helmut Bender proved that F *(G)F^*(G) itself enjoys these properties.

Named after Hans Fitting.

Created on November 10, 2010 23:21:25 by Urs Schreiber (87.212.203.135)