§ V

Abstract

A commutative (or “abelian”) group is a set G, together with a binary operation between elements of G, satisfying the following axioms (in which the group operation is denoted by +):

• I I (Associativity). (x+y) + z = x +(y + z) for all x,y,z in G.

• II (Commutativity). x+y=y + x for all x,y in G.

• III If x,y are in G, the equation x+z=y has a unique solution z in G (written z=y-x).

• IV There is an element in G, called the neutral element (and denoted by 0) such that 0+x=x for all x in G.