{Some simple projective Brauer quotients of simple modules
      for the symmetric groups in characteristic two}
\author{Luis Valero-Elizondo}
\address{Mathematics Department \\
   University of Georgia \\
   Athens, GA 30602}


\begin{abstract}
   By Alperin's weight conjecture~\cite{af} the number of
   simple $kS_n$-modules equals the number of weights for
   $S_n$, where $S_n$ is the symmetric group on $n$ symbols
   and $k$ is a field of characteristic $p>0$. In this paper
   we answer the question ``when is the Brauer quotient of a
   simple $F_2S_n$-module $V$ with respect to a subgroup $H$ of
   $S_n$ both simple and projective as an $N_{S_n}(H)/H$-module?'',
   in some special cases. Remarkably, in
   each case there is only one such subgroup $H$ (up to conjugacy).
\end{abstract}

STATUS: This paper has been accepted for publication in the
Journal of Algebra.