A p-subgroup is a specific type of subgroup in group theory, a branch of mathematics. It is defined as a subgroup where the order (the number of elements) is a power of a prime number p. This means that if you take any subgroup of a group, and its size can be expressed as p^n (where n is a non-negative integer), then it is considered a p-subgroup. P-subgroups are important in the study of finite groups, particularly in the context of the Sylow theorems. These theorems provide information about the existence and number of p-subgroups within a finite group, helping mathematicians understand the structure and classification of groups more effectively.