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Facts used
==Facts used==
# [[uses::Cyclic implies Aut-Abelianabelian automorphism group]]: The automorphism group of a cyclic group is Abelian.# [[uses::Inverse map is automorphism iff Abelianabelian]]: For an Abelian group, the map sending every element to its inverse is an automorphism.
# [[uses::kth power map is bijective iff k is relatively prime to the order]]
 
==Proof==
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