How to Find Elements of U(12) for Constructing a Cayley Table?

[Benzoate]

Homework Statement

Construct a cayley table for U(12)

Homework Equations

No equations necessary for this kind of table

The Attempt at a Solution

I could construct a cayley table , but I have no idea how to determine what elements are in U(12). What method would you apply hear to find the elements of the group U(12). My textbook does a poor job of explaining exactly how to determine what elements and how many elements are in U(12)

 

[d_leet]

Is U(12) supposed to be the group of units modulo 12? If so then what elements are units in the group Z₁₂? Maybe a better question is what is a unit?

 

[Benzoate]

Is U(12) supposed to be the group of units modulo 12? If so then what elements are units in the group Z₁₂? Maybe a better question is what is a unit?

when you say elements in Z(sub 12) do you mean the multiples of 12(i.e, 12,24,36, etc)

 

[matt grime]

That would be 12Z. Z_{12} is, in this case Z/12Z, or the set {0,1,2...,11} with addition and multiplcation mod 12. U_12 is the subset ot Z/12Z of elements that are units, i.e. it is the set of numbers in {0,1,..,11} that a coprime with 12, with the group operation of multiplication.

Frequently, if you are short of a definition, then google will give the answer.