👉 In mathematics, a set X is said to be a subgroup of a group G if for every element x in X, there exists an element y in G such that xy = x. This operation is called the composition of elements. The concept of a coset is particularly useful when studying groups and their structure. The set of all elements that are fixed by the action of a group G on itself under multiplication is known as the cosets or quotients of X by G. For example, if
