Groups associated with modules over nearrings

We construct a group $D(I,T)$ associated with the pair $(I,T)$, where $I$ is a nontrivial distributive submodule of a left $N$-module $G$ $T$ is a nontrivial subgroup of the unit group $U(N)$ of a right nearring $N$ with an identity element, and find criteria for $D(I,T)$ to be a Frobenius group.