Endomorphism monoid

Definition
The endomorphism monoid of a group is the monoid defined as follows:


 * Its elements are the endomorphisms of the group.
 * Its identity element is the identity map from the group to itself.
 * Multiplication is by function composition.

The elements of the endomorphism monoid with two-sided inverses form a subgroup of the endomorphism monoid and this subgroup is the automorphism group of the original group.