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

(a*b)*c = a*(b*c)
if a, b, c are in Group G

Definition of AssociativityEdit

Let G be a group with binary operation  



  1. If a, b, c are in G, (a   b)   c = a   (b   c)


  1. G has to be a group
  2. All of a, b and c have to be elements of G.
  3.   has to be the binary operation of G
  4. The converse is not necessary true:
a (a   b)   c = a   (b   c) does not mean a, b or c must be in G.