# Constructing a cayley table

1. Aug 29, 2007

### Benzoate

1. The problem statement, all variables and given/known data

Construct a cayley table for U(12)
2. Relevant equations

No equations necessary for this kind of table

3. 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)

2. Aug 30, 2007

### 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?

3. Aug 30, 2007

### Benzoate

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

4. Aug 30, 2007

### 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.