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Constructing a cayley table

  1. Aug 29, 2007 #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. Aug 30, 2007 #2
    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. Aug 30, 2007 #3
    when you say elements in Z(sub 12) do you mean the multiples of 12(i.e, 12,24,36, etc)
  5. Aug 30, 2007 #4

    matt grime

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    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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