On the irreducible representations of soluble groups of finite rank
  We obtained some sufficient and necessary conditions of existence of faithful irreducible representations of a soluble group $G$ of finite rank over a field $k$. It was shown that the existence of such representations strongly depends on construction of the socle of the group $G$. The situation is especially complicated in the case where the field $k$ is locally finite. 
A. V. Tushev
math.GR