(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find all the automorphisms of a cyclic group of order 10.

2. Relevant equations

ψ(a)ψ(b)=ψ(ab)

For G= { 1, x, x^2,..., x^9}, and some function

ψ(a) = x^(a/10)

3. The attempt at a solution

I know that a homomorphism takes the form

Phi(a)*phi(b) = phi (ab) , and that an automorphism maps from G->G,

However, I don't understand what an automorphism for a cyclic group would even look like. I suppose it should be something of the form:

ψ(a) = x^(a/10)

and that a should be a specific power, but I have no idea where to go from here.

I appreciate any help. Thanks

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# Find All Automorphisms of Cyclic Group of Order 10

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