J. Aust. Math. Soc.
77 (2004), 401-423
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Modular Lie representations of finite groups
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Abstract
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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
 denote the
n th homogeneous component of the free Lie
K-algebra generated by (a basis of)
V. Then
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
up to isomorphism.
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