 A very important consequence of Theorem 3 is that the condition "np" = 1 is equivalent to saying that the Sylow "p"-subgroup of "G" is a normal subgroup
(there are groups that have normal subgroups but no normal Sylow subgroups, such as "S"4).There is an analogue of the Sylow theorems for infinite groups.We define a Sylow "p"-subgroup in an infinite group to be a "p"-subgroup (that is, every element in it has "p"-power order) that is maximal for inclusion among all "p"-subgroups in the group.