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Electromech1
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Homework Statement
Find all the automorphisms of a cyclic group of order 10.
Homework Equations
ψ(a)ψ(b)=ψ(ab)
For G= { 1, x, x^2,..., x^9}, and some function
ψ(a) = x^(a/10)
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