When p is a prime number, then a p-group is a group, all of whose elements have order some power of p. For a finite group, the equivalent definition is that the number of elements in G is a power of p. In fact, every finite group has subgroups which are p-groups by the Sylow theorems, in which case they are called Sylow p-subgroups.

group | group direct product | group order | Sylow p-subgroup | Sylow theorems