
#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: 9,398

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. 


Register to reply 
Related Discussions  
Constructing a Table. (Radioactivity)  General Physics  2  
Cayley digraph  Calculus & Beyond Homework  0  
cayley hamilton  Linear & Abstract Algebra  7  
Deligne Dam of Cayley River  Calculus & Beyond Homework  2  
cayley  hamilton theorem  Linear & Abstract Algebra  7 