M. E. Harris and M. Linckelmann
On the Glauberman and Watanabe correspondences for blocks
of finite $p$-solvable groups


\abstract If $G$ is a finite $p$-solvable group for some prime $p$,
$A$ a solvable subgroup of
the automorphism group of $G$ of order prime to $\vert G\vert$
such that $A$ stabilises a $p$-block $b$ of $G$ and acts
trivially on a defect group $P$ of $b$, then there is a Morita
equivalence between the block $b$ and its Watanabe correspondent
$w(b)$ of $C_G(A)$, given by a bimodule $M$ with vertex
$\Delta P$ and an endo-permutation module as source, which on the
character level induces the Glauberman correspondence (and which
is an isotypy by Watanabe's results in [24]).
\endabstract