J. Aust. Math. Soc.
77 (2004), 401423

Modular Lie representations of finite groups


Abstract

Let K
be a field of prime characteristic
p and let
G be a finite group with a Sylow
psubgroup of order
p. For any finitedimensional
KGmodule
V and any positive integer
n, let
denote the
n th homogeneous component of the free Lie
Kalgebra generated by (a basis of)
V. Then
can be considered as a
KGmodule, 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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