Group theory question
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Group theory question

[From: ] [author: ] [Date: 13-10-31] [Hit: ]
the automorphism is the identity map.I hope this helps!......
If G is a group having only two elements then why does the automorphism A(G) consists of only I (identity)?

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An automorphism is a bijective homomorphism from G to itself.

Under any homomorphism, the identity must get sent to itself.
Since G only has one other element, and the automorphism is 1-1 and onto, this implies that this second element must also get mapped to itself.

So, the automorphism is the identity map.

I hope this helps!
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