# nLab generalized Fitting subgroup

One definition of the generalized Fitting subgroup $F^*(G)$ of a group $G$ is that it is the subgroup generated by all normal subgroups $N$ of $G$ possessing subgroups $N_1,N_2,\dots, N_r$ for some integer $r$ such that $N=N_1N_2\cdots N_r$; $x_i x_j=x_j x_i$ for all $x_i\in N_i$, $x_j\in N_j$, and distinct subscripts $i$ and $j$; and each $N_i$ either has prime power order or is a quasisimple group. Helmut Bender proved that $F^*(G)$ itself enjoys these properties.

Named after Hans Fitting.

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