Endomorphism monoid
From Groupprops
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.
