Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Closure
![](http://upload.wikimedia.org/wikipedia/commons/thumb/8/86/Algebra_Proof_Diagram_Closure.svg/180px-Algebra_Proof_Diagram_Closure.svg.png)
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]- If a, b are in G, a b is in G.
Notice
[edit | edit source]- G has to be a group
- Both a and b have to be elements of G.
- has to be the binary operation of G
- The converse is not necessary true:
- a b is in G does not mean a or b must be in G.