Euler phi function

[ttamarl]

Haven't even covered this in class yet, but it's on the homework anyway. Please help! thanks!

Prove that Aut(Z_n) is isomorphic to U_{phi_n}, where phi_n is the
Euler phi-function.
U_{phi_n} is not in general cyclic- it is abelian.
It is however, cyclic if n is a prime

 

[daon]

Consider posting in a thread whetehr or not you've been helped. Posting threads with no work and no clarification does no one any good.

Z_n has Phi(n) generators. Sending the identity of a cyclic group to a generator creates an isomorphism if the cardinalities are identical. Since it is from Z_n to itself it is an automorphism. Hence there are Phi(n) automorphisms on Zn.

I'll let you think about that and report back before I help any more.

 

[daon]

Haven't even covered this in class yet, but it's on the homework anyway. Please help! thanks!

Prove that Aut(Z_n) is isomorphic to U_{phi_n}, where phi_n is the
Euler phi-function.
U_{phi_n} is not in general cyclic- it is abelian.
It is however, cyclic if n is a prime

Also, as stated it is WRONG. I know what was meant and the above post should be read to reflect that and not what you wrote.