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 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...