Flat modules over group rings of finite groups
D.~J.~Benson
Department of Mathematics, University of Georgia, 
Athens GA 30602, USA

\begin{abstract}
Let $k$ be a commutative ring of coefficients and $G$ be a finite 
group. Does there exist a flat $kG$-module which is projective
as a $k$-module but not as a $kG$-module? We relate this question
to the question of existence of a $k$-module which is flat and
periodic but not projective. For either question to have a 
positive answer, it is at least necessary to have $|k| \ge 
\aleph_\omega$. There can be no such example if $k$ is Noetherian
of finite Krull dimension, or if $k$ is perfect.
\end{abstract}