Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Associativity

frame| Associativity: (a*b)*c = a*(b*c) if a, b, c are in Group G Definition of Associativity Let G be a group with binary operation Usage Usage1If a, b, c are in G, (a b) c = a (b c) Notice G has to be a group All of a, b and c have to be elements of G. has to be the binary operation of G The converse is not necessary true: a (a b) c = a (b c) does not mean a, b or c must be in G.