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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

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

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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.

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The solution of the Posting is in the attached file.

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 provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
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