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Definition of Group:
A set G whose elements can be combined together in way similar to the addition of integers. If the result of combining the elements a and b of G is denoted by a*b, then G will be a group if and only if the operation * satisfies the following four properties:
1: any two elements in the set can be combined by the operation * to produce a unique third element in the set;
2: the operation is associative: given any three members a, b and c of G then a*(b*c) = (a*b)*c;
3: there is a special element I, called the identity element, such that for any element a, a*I=I*a=a;
4: corresponding to each element a, there is an element a', called the inverse of a (and depending upon a), such that a*a'=a'*a=I
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