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

From Wikibooks, open books for an open world
Jump to navigation Jump to search
a*b is in G if a, b are in Group G

Definition of Closure[edit | edit source]

Let G be a group with binary operation

Usage[edit | edit source]

  1. If a, b are in G, a b is in G.

Notice[edit | edit source]

  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.