On the local behavior of mappings with unbounded quasiconformality coefficient

We study space mappings more general than the mappings with bounded distortion in the sense of Reshetnyak. We consider questions related to the local behavior of mappings differentiable almost everywhere, possessing Properties $N$, $N^{-1}$, $ACP$, and $ACP^{-1}$, and such that quasiconformality coefficient satisfies a certain restriction on growth. We show that the value of a mapping satisfying these requirements on an arbitrary neighborhood of an essential singularity can be greater in absolute value than the logarithm of the inverse radius of the ball raised to an arbitrary positive power.