Group of Math
Definition
Group (G, *) is a set G, together with a binary operation * on G, such that the following axioms are satisfied:
- The bianary operation * is associative
- There is an element e in G such that e * x = x * e = x for all x € G. (This element e is an identity element for * on G)
- For each a an G, there is an element a’ is an inverse of a with the property that a’ * a = a * a’ = e
Note:
Many books have another axiom for a group, namely that G is closed under the operation *, that is (a*b) € G for all a, b € G
