What four properties are needed to form a mathematical group?

Answer 1

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