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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