411 REFERENCE · Wikibooks
Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Closure
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
frame| Closure: a*b is in G if a, b are in Group G
Definition of Closure
Let G be a group with binary operation
Usage
Usage1If a, b are in G, a b is in G.
Notice
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.