Restricted Lie algebras of polycyclic groups, II

Abstract

This is the second paper in the series of three. We study restricted Lie algebras of polycyclic groups and obtain conditions for existence of $p$-series with associated restricted Lie algebra abelian or free abelian with rank equal to the Hirsch number of the group. We develop methods for constructing such series, these methods are based on construction of filtrations and valuation functions in the group rings.