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Constructing a cayley table

by Benzoate
Tags: cayley, constructing, table
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Benzoate
#1
Aug29-07, 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)
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d_leet
#2
Aug30-07, 12:39 AM
P: 1,075
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?
Benzoate
#3
Aug30-07, 07:26 AM
P: 569
Quote Quote by d_leet View Post
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?
when you say elements in Z(sub 12) do you mean the multiples of 12(i.e, 12,24,36, etc)

matt grime
#4
Aug30-07, 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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