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 $N=N_1{N}_2\cdots N_r$; $x_i{x}_j=x_j{x}_i$ 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.