The existence of Hall subgroups can be proved by induction on the order of "G", using the fact that every finite solvable group has a normal elementary abelian subgroup. More precisely, fix a minimal normal subgroup "A", which is either a "π"-group or a "π'"-group as "G" is "π"-separable. By induction there is a subgroup "H" of "G" containing "A" such that "H"/"A" is a Hall "π"-subgroup of "G"/"A". If "A" is a "π"-group then "H" is a Hall "π"-subgroup of "G". On the other hand, if "A" is a "π'"-group, then by the Schur–Zassenhaus theorem "A" has a complement in "H", which is a Hall "π"-subgroup of "G".