subgroup definition
The equivalence of this definition with the earlier one is often called the subgroup condition. For full proof, refer: Sufficiency of subgroup condition. It has two forms (left and right): A subset of a group is termed a subgroup if it is nonempty and is closed under the left quotient of elements. In other words, a subset of a group is termed a subgroup if and only if is nonempty and whenever. A subset of a group is termed a subgroup if it is nonempty and is closed under the right quotient of elements.