GROUPS 6

Example 3 :

The following examples give groups with their respective tables.

1. Group V = {e,a,b,c} under multiplication (.). This group is the Klein 4-group. (notation V comes from the German word for four).

Example 4 :

Let S = {a,b,c}. Operation * is defined on S by the following table :

Determine whether * is commutative on S.


Solution :

From the table, a*b = c and b*a = a.

Since, a*b is not equal to b*a, then * is not commutative on set S.


Note : A binary operation defined by a table is commutative if and only if the entries in the table is symmetric with respect to the diagonal that starts at the upper left corner of the table and terminates at the lower right corner.