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

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

Definition of Associativity[edit]

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.