Non-Hopfian group
= Non-Hopfian group
A non-Hopfian group admits a surjective <endomorphism> which is not injective. The <Baumslag-Solitar group> $BS(2,3)$ has such an endomorphism $a\mapsto a^2$, $t\mapsto t$: its image contains $a^2$ and $a^3$, while the nonidentity <commutator> $[a,tat^{-1}]$ lies in its kernel by <Britton's lemma>.