[Tutor] Having Python figure out whether a set is a group

[Julieta Rangel]

Given the following table, how can I make the computer verify whether the 
following set is a group or not?  The set is G = {e,a,b,ab)
The table under the binary operation * with the elements of the set looks 
like:

         *_|     e    a    b    ab
         ---------------------------
          e|     e    a    b    ab
          a|     a    e    ab   b
          b|     b    ab   e    a
         ab|     ab   b    a    e

The computer would have to check the 4 properties of groups (closure, 
associativity, identity element, and inverse element).  By the way, the set 
G is in fact a group. It is closed under the binary operation (a * b = ab, 
and ab is in G, b * ab =a and a is in G, etc), it is associative (a * (b * 
ab) = (a * b) * ab; e * (a * b) = (e * a) * b, etc), it has an identity 
element e (a * e = a, b * e = b, ab * e = ab, e * e = e), and every element 
is an inverse of itself (Note: a*a = e, b*b = e, ab*ab = e, and e*e = e).How 
could the computer check for closure?  I'm assuming the computer would have 
to go through the elements in the table and compare them with the original 
set.  How could this be done?  This problem requires some thinking.  Does 
anyone want to help or do you know where I can go for help?

Julieta

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