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Answering a question of Elekes and Vidny\'anszky, we construct a Polishmeta-abelian group $H$ and a subgroup $F\subset H$, which is a Haar null$F_\sigma$-set in $H$ that cannot be enlarged to a Haar null $G_\delta$-set.

A Polish group containing a Haar null $F_\sigma$-subgroup that cannot be enlarged to a Haar null $G_\delta$-set