Finite p-Groups and Lie Algebras

Abstract

The character of this chapter is almost entirely that of a survey, and in it we shall outline the shape of the linear methods in finite group theory that have a direct bearing on our principal theme, the restricted Burnside problem. The only subject treated in any detail in M. R. Vaughan-Lee’s elegant approach to describing the multilinear identities of the Lie algebra L(B(d, p)) associated with the Burnside group B(d, p). In particular, it is proved by elementary methods (see Corollary 2.3 in § 3) that L(B(d, p)) satisfies E_p-1. The solution of RBP provided here is therefore independent of other sources.