I am currently reading on some theorems about relations between finite group and its largest cardinality of independent generating sequence. One assumed-well-known result is that if given a finite Frattini free group $G$ (Frattini free means the intersection of all maximal subgroups is trivial), then the Fitting subgroup $F(G)$ is abelian and complemented. Also, $F(G)$ is a direct product of minimal normal subgroups of G.
Definition: if $G$ is finite, then the Fitting subgroup is the subgroup generated by all nilpotent normal subgroups of G.
Currently, I do not know why the result stated above is true. Any comment or guide is greatly appreciated.