J. Aust. Math. Soc.  77 (2004), 401-423
Modular Lie representations of finite groups

R. M. Bryant
  School of Mathematics
  University of Manchester
  PO Box 88
  Manchester M60 1QD

Let K be a field of prime characteristic p and let G be a finite group with a Sylow p-subgroup of order p. For any finite-dimensional KG-module V and any positive integer n, let $L^n(V)$ denote the n th homogeneous component of the free Lie K-algebra generated by (a basis of) V. Then $L^n(V)$ can be considered as a KG-module, called the n th Lie power of V. The main result of the paper is a formula which describes the module structure of $L^n(V)$ up to isomorphism.
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