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Let G$G$ be a group which is Hopfian and given a short exact sequence 1---> F---> H$1\to F \to H \to G \to 1$
with---> G--> 1
with F$F$ a finite normal subgroup of H$H$. Is H$H$ Hopfian?
Let G be a group which is Hopfian and given a short exact sequence 1---> F---> H---> G--> 1
with F a finite normal subgroup of H. Is H Hopfian?
Let $G$ be a group which is Hopfian and given a short exact sequence $1\to F \to H \to G \to 1$
with$F$ a finite normal subgroup of $H$. Is $H$ Hopfian?
