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

Abstract

We describe the upper and lower Lie nilpotency index of a modular group algebra FGof some metabelian groupGand 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 FGwith group of units of class 3 is given, which was obtained by Rao and Sandling for finite groupsG. © 1999 Academic Press.