Group theory

Group theory is the area of mathematics which deals directly with the study of groups.

In order for a set G 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 G. 2)G has an has an identity element j under * such that for any element a in G, j*a=a*j=a. 3)The operation is associative, which means for any three elements a, 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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