Authors' name: Martin Hertweck

Institution: Universitaet Stuttgart, Germany

Title: A new proof of Glauberman's Z$^{\ast}$-theorem

Short abstract of the paper:

It is shown that for a finite group $G$ of order divisible by a prime $p$,
an algebraically closed field $k$ of characteristic $p$ and $H\leq G$
such that the summand of the induced module $k_{H}\uparrow^{G}$ which belongs
to the principal block of $kG$ is just the trivial $kG$-module $k_{G}$, the
indecomposable projective $kG$-module which covers $k_{G}$ is also a 
projective cover of $k_{H}$; 
in particular, $[G,\mbox{Z}(H)]\leq\mbox{O}_{p^{\prime}}(G)$.
When combined with a recent result of John Murray this yields 
another proof of Glauberman's Z$^{\ast}$-theorem.

Current status: preprint, submitted