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!
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!