Constructing a cayley table

  1. 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. jcsd
  3. 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?
  4. when you say elements in Z(sub 12) do you mean the multiples of 12(i.e, 12,24,36, etc)
  5. matt grime

    matt grime 9,395
    Science Advisor
    Homework Helper

    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.
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