# Aut(G), the set of automorphisms of G, is also a group.

Modern Algebra

Group Theory (LXX)

The Set of all Automorphisms of a Group

If G is a group, then Aut(G), the set of automorphisms of G, is also a group.

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Modern Algebra

Group Theory (LXX)

The Set of all Automorphisms of a Group

By:- Thokchom Sarojkumar Sinha

If is a group, then , the set of automorphisms of , is also a group.

Solution:- Let be arbitrary.

Closure Property

are one-one onto

is one-one onto.

For all ,

and

Then

Thus

Hence

Associativity

...

#### Solution Summary

It is proven that if G is a group, then Aut(G), the set of automorphisms of G, is also a group. The solution is detailed and well presented.