So I've been reading a bit about automorphisms today and I was wondering about something. I'm particularly talking about groups in this case, say a group G.(adsbygoogle = window.adsbygoogle || []).push({});

So an automorphism is a bijective homomorphism ( endomorphism if you prefer ) of a group G.

We use Aut(G) to denote the set of all automorphisms of G.

There is also an inner automorphism induced by a in G. The map f := G → G such that f(x) = axa^{-1}for all x in G is called the inner automorphism of G induced by a.

We use Inn(G) to denote the set of all inner automorphisms of G.

My question now :

If |G| is infinite, are the orders of Aut(G) and Inn(G) also infinite? It makes sense to me that they would be.

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# Question about automorphisms

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