# (N)T is a normal subgroup of G.

Modern Algebra

Group Theory (LXVI)

Automorphism of a Group

Let G be a group, T an automorphism of G, N a normal subgroup of G. Prove that (N)T is a normal subgroup of G.

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Modern Algebra

Group Theory (LXVI)

Automorphism of a Group

By:- Thokchom Sarojkumar Sinha

Let be a group, an automorphism of , a normal subgroup of .

Prove that is a normal subgroup of .

Solution:- Let , where is a ...

#### Solution Summary

It is proven that (N)T is a normal subgroup of G where G is a group, T an automorphism of G and N a normal subgroup of G.

The solution is detailed and well presented.