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Constructing a cayley table 
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#1
Aug2907, 08:57 PM

P: 569

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
Aug3007, 12:39 AM

P: 1,076

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



#3
Aug3007, 07:26 AM

P: 569




#4
Aug3007, 08:24 AM

Sci Advisor
HW Helper
P: 9,396

Constructing a cayley table
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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