Lie properties of the group algebra and the nilpotency class of the group of units

We describe the upper and lower Lie nilpotency index of a modular group algebra FG of some metabelian group G and apply these results to determine the nilpotency class of the group of units, extending certain results of Shalev without restriction to finite groups. A characterization of modular group algebras FG with group of units of class 3 is given, which was obtained by Rao and Sandling for finite groups G. (C) 1999 Academic Press.