sentences:  One of the most important examples of this is Philip Hall's 1937 theorem on the existence of Sylow systems for soluble groups.This shows that every soluble group is a Zappa–Szép product of a Hall "p'"-subgroup and a Sylow "p"-subgroup, and in fact that the group is a (multiple factor) Zappa–Szép product of a certain set of representatives of its Sylow subgroups.In 1935, George Miller showed that any non-regular transitive permutation group with a regular subgroup is a Zappa–Szép product of the regular subgroup and a point stabilizer.