Commutator Group

• Let be a group.

  An element that can be expressed as

  is called a commutator in .

• The Subgroup which consists of all commutators is called the commutator subgroup of .

• (Fraleigh 15.20) The commutator subgroup is a normal subgroup of .

  If is a normal subgroup of , then is Abelian if and only if .

Links §

• A First Course in Abstract Algebra 7th Edition by Fraleigh