Normal Subgroups

Let $$G$$ be an abelian group, the composition in $$G$$ being denoted multiplicatively. Let $$H$$ be any subgroup of $$G$$…. Click here to read more

Theorem 1: A subgroup $$N$$ of a group $$G$$ is normal if and only if $$xN{x^{ – 1}} = N\,\,\,\,\forall… Click here to read more

Definition: The set $$Z$$ of all those elements of a group $$G$$ which commute with every element of $$G$$ is… Click here to read more

Definition: If $$G$$ is a group and $$N$$ is a normal subgroup of group $$G$$, then the set $$G|N$$ of… Click here to read more

Example 1: If $$H$$ is a normal subgroup of a finite group $$G$$, then prove that \[o\left( {G|H} \right) =… Click here to read more

Conjugate Element: If $$a,b \in G$$, then $$b$$ is said to be a conjugate of $$a$$ in $$G$$ if there… Click here to read more