A subgroup H of a group G is a normal subgroup of G if and only if ghg^-1 ∈ H ∀ g∈G and h∈H.

Check out other Group theory lectures here :-
Inverse of each element of group is unique | Group Theory | NERDY CREW
• Inverse of each elemen...
Centre of a group.The centre of a group G is a subgroup of G | NERDY CREW
• Centre of a group.The ...
Fermat’s theorem with examples in group theory | NERDY CREW
• Fermat’s theorem with ...
Properties of group( Identity element in group is unique) BSc Maths | GROUP THEORY | NERDY CREW
• Properties of group( I...
Let (G,*) be a group.Then cancellation law holds in Group | NERDY CREW
• Let (G,*) be a group.T...
Euler’s function and euler’s theorem in group theory | NERDY CREW
• Euler’s function and e...
Let G be a finite group and a∈G. Then a^ O(G) = e | GROUP THEORY | NERDY CREW
• Let G be a finite grou...