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

a*b is in G if a, b are in Group G

Definition of ClosureEdit

Let G be a group with binary operation  



  1. If a, b are in G, a   b is in G.


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