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Let [tex]\theta:G->G'[/tex] be an isomorphism between G and G', where o(G)=m=o(G'), and both G and G' are cyclic, i.e. G=[a] and G'=

So my question is, when we want to find the total number of isomorphisms from G to G', i 'know' that the total number of such isomorphisms is basically

the number of generators of G':

[tex]\theta(a)=b^k[/tex] where gcd(k,m)=1. But i don't really understand why? That is, how are we sure that by just counting the number of generators on G' we are actually finding the total number of such isomorphisms. ?

Any explanations would be appreciated.

So my question is, when we want to find the total number of isomorphisms from G to G', i 'know' that the total number of such isomorphisms is basically

the number of generators of G':

[tex]\theta(a)=b^k[/tex] where gcd(k,m)=1. But i don't really understand why? That is, how are we sure that by just counting the number of generators on G' we are actually finding the total number of such isomorphisms. ?

Any explanations would be appreciated.