Groups associated with modules over nearrings

Abstract

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.