Retract (group theory)
In mathematics, in the field of group theory, a subgroup of a group is termed a retract if there is an endomorphism of the group that maps surjectively to the subgroup and is identity on the subgroup. In symbols, is a retract of if and only if there is an endomorphism such that for all and for all.
The endomorphism itself is an idempotent element in the transformation monoid of endomorphisms, so it called an idempotent endomorphism or a retraction.
The following is known about retracts:
