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    Is the group aut(Z_10) a permutation group?

    (Original post by B_9710)
    Is the group aut(Z_10) a permutation group?
    Throwing a theorem at the problem: the automorphism group of a finite cyclic group of order n is itself of order \phi(n) (Euler totient function). In fact the automorphism group of a cyclic group is itself cyclic under certain conditions (n = 2, 4, the power of an odd prime, or twice the power of an odd prime).

    So here (if I can count properly this early in the morning), we have:

    Aut(\mathbb{Z}_{10}) = \mathbb{Z}_{4}

    Can you finish the question off?

    n.b. If you don't want to throw the above theorem at this problem, you need to think about how generators of the original group relate to automorphisms.
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Updated: November 1, 2015
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