Recent content by Hugheberdt

Thank you morphism. I did notice myself yesterday that phi(1026)=18^2. However, I could not deduce why there are no elements in G of order greater than 18. The homework is already due and I will have it corrected and commented soon. But if someone still feels like coming up with...

Homework Statement We are given the ring Z/1026Z with the ordinary addition and multiplication operations. We define G as the group of units of Z/1026Z. We are to show that g^{18}=1. Homework Equations The Euler-phi (totient) function, here denoted \varphi(n) The Attempt at a Solution...

Thank you both! You were both very helpful! I feel like I've got a better grasp of it now.

Thank you Dick for this somewhat different viewpoint! I'd just like to check a few things to make sure I've got them right (I suspect they are correct, but just to check): 1.The elements 3 and 7 both have order 4, \bullet modulo 20, so both would do as generators (but not 1 and 9, with...

Homework Statement I am given the group (G,\bullet) consisting of all elements that are invertible in the ring Z/20Z. I am to find the direct product of cyclic groups, which this group G is supposedly isomorphic to. I am also to describe the isomorphism. Homework Equations The...