Endomorphism

An endomorphism is a morphism from a mathematical object $A$ into itself. The set of all endomorphisms is denoted by $End(A)$.
If $G$ is a group then $End(G)$ is a ring, with the sum being the group operation and the product the composition of endomorphisms. The group $G$ can be see as a $End(G)$-module, and given any subring $S\subset End(G)$ we have an $S$-module structure in $G$.

An endomorphism that is also an isomorphism is an automorphism.