A Note on the Hopficity of Finitely Generated Free-by-Nilpotent Groups
James Boler · Canadian Mathematical Bulletin · 1977
Our purpose is to deduce from a theorem of P. Hall the following observation. Let G be a finitely generated group and F a free normal subgroup of G with G/F nilpotent. Then G is hopfian. Here a group G is hopfian if every epiendomorphism G→G is an automorphism.