Faithful Representations of Lie Algebras over Power Series

This is an exposition of the authors doctoral thesis completed at the University of Oklahoma under the direction of Professor Andy Magid. We begin with a brief discussion of the work done by Dixon, Du Sautoy, Mann and Segal (DDMS) in showing that powerful pro-p groups are almost linear over the p-adic integers Z _p . That is, G has a subgroup of finite index which injects into Gl _d (Z _p ) [3, Cor. 4.19, p.73].