On Value Distributions for Quasimeromorphic Mappings on $\mathbb{H}$-type Carnot Groups

In the present paper we define quasimeromorphic mappings on homogeneous groups and study their properties. We prove an analogue of results of L. Ahlfors, R. Nevanlinna and S. Rickman, concerning the value distribution for quasimeromorphic mappings on $\mathbb{H}$-type Carnot groups for parabolic and hyperbolic type domains.