Normal Subgroups Let be an abelian group, the composition in being denoted multiplicatively. Let be any subgroup of . If is an... Click here to read more

Theorems of Normal Subgroups Theorem 1: A subgroup of a group is normal if and only if . Proof: Let , then . Therefore... Click here to read more

Center of a Group Definition: The set of all those elements of a group which commute with every element of is called the center... Click here to read more

Quotient Groups Definition: If is a group and is a normal subgroup of group , then the set of all cosets of... Click here to read more

Examples of Quotient Groups Example 1: If is a normal subgroup of a finite group , then prove that Solution: number of distinct right... Click here to read more

Conjugacy in a Group Conjugate Element: If , then is said to be a conjugate of in if there exists an element such that... Click here to read more