The nilpotency class of the unit group of a modular group algebra. II (Q584356)

For a finite p-group G, let U(G) be the unit group of the group algebra of G over a field of p elements. It is known that if \(| G'| =p\), the nilpotency class of U(G) is p. The main result of the present paper states, that if \(| G'| >p\), the same nilpotency class is at least 2p-1. Equality holds if G has class 2 and \(| G'| =p^ 2\) [part I, by \textit{A. Shalev} alone, is also going to appear in the same Journal].