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17.50 (2010)

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Is it true that for every finite group $G$, there is a finite group $F$ and a surjective homomorphism $f : F \to G$ such that for each nontrivial subgroup $H$ of $F$, the restriction $f|_H$ is not injective?

It is known that for every finite group $G$ there is a finite group $F$ and a surjective homomorphism $f : F \to G$ such that for each subgroup $H$ of $F$ the restriction $f|_H$ is not bijective.

Contributor: E. G. Zelenyuk

Progress

Yes, it is (V. P. Burichenko, Math. Notes, 92, no. 3 (2012), 327–332).

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