Group theory
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Group theory is the area of mathematics which deals directly with the study of groups.
In order for a set 
to be considered a group, it must have the following four properties:
1) An operation 
(such as addition or multiplication, although multiplication is standard) is defined on .
2) has an has an identity element 
under such that for any element 
in , 
.
3)The operation is associative, which means for any three elements , b, and c in G, (a*b)*c=a*(b*c)
4)Every element a in G has an inverse "x" under * that is also in G such that a*x=x*a=j.
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