A p-subgroup is a subgroup of a group whose order (the number of elements) is a power of a prime number p. In group theory, p-subgroups play a crucial role in understanding the structure of finite groups, particularly through the Sylow theorems, which provide information about the existence and number of such subgroups. For example, if a group has an order of 30, its p-subgroups could be of order 3 (since 3 is a prime) or 5. These subgroups help mathematicians analyze the properties of the larger group and can reveal important information about its composition and behavior.