J. Aust. Math. Soc.
79 (2005), 257276

The problem revisited

Thomas Michael Keller
Department of Mathematics
Texas State University
601 University Drive
San Marcos, TX 78666
USA
keller@txstate.edu



Abstract

Suppose that the finite group
acts faithfully and irreducibly on the finite
module
of characteristic p
not dividing
. The wellknown
problem states that in this situation, if
is the number of conjugacy classes of the
semidirect product
, then
. For
psolvable groups, this is equivalent to Brauer's
famous
problem. In 1996, Robinson and Thompson proved
the
problem for large
p. This ultimately led to a complete proof of the
problem. In this paper, we present a new proof
of the
problem for large
p.

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