Subgroup

In group theory, a branch of mathematics, given a group <math>G</math> under a binary operation, a subset <math>H</math> of <math>G</math> is called a subgroup of <math>G</math> if the elements <math>H</math> also forms a group under the binary operation.

The situation could arise in which the subset <math>H</math> does not comply with the binary operation. In that case, H would not be a subgroup.

For example, the even numbers are a subgroup of the integers, with addition as the binary operation.