The nilpotency class of the unit group of a modular group algebra. III (Q1325289)

The author continues the study of the nilpotency class of the unit group of a modular group algebra [Part I, Isr. J. Math. 70, 257-266 (1990; Zbl 0713.16020); Part II, ibid., 267-277 (1990; Zbl 0693.16008)]. A recent result of \textit{X. Du} [Can. Math. Bull. 35, 174-179 (1992; Zbl 0801.16019)] combined with that of \textit{A. K. Bhandari} and the reviewer [Bull. Lond. Math. Soc. 24, 68-70 (1992; Zbl 0777.20004)] shows that the nilpotency class of the unit group is determined by the orders of the Lie dimension subgroups, provided the characteristic \(\geq 5\). Exploiting the techniques developed earlier by the author for the study of Lie dimension subgroups [J. Lond. Math. Soc., II. Ser. 43, 23-46 (1991; Zbl 0669.16015)], some very interesting further results are obtained for the nilpotency class of the unit groups of group algebras under the above restriction on the characteristic.