 Schur–Zassenhaus theorem

The Schur–Zassenhaus theorem is a theorem in group theory which states that if formula_1 is a finite group, and formula_2 is a normal subgroup whose order is coprime to the order of the quotient group formula_3, then formula_1 is a semidirect product (or split extension) of formula_2 and formula_3.An alternative statement of the theorem is that any normal Hall subgroup formula_2 of a finite group formula_1 has a complement in formula_1.