A block theoretic analogue of a theorem of Glauberman and Thompson
Radha Kessar and Markus Linckelmann
May 2001

Abstract. If $p$ is an odd prime, $G$ a finite group and $P$ a 
Sylow-$p$-subgroup of $G$, a theorem of Glauberman and Thompson 
states that $G$ is $p$-nilpotent if and only if $N_G(Z(J(P)))$ is 
$p$-nilpotent, where $J(P)$ is the Thompson subgroup of $P$ generated 
by all abelian subgroups of $P$ of maximal order. Following a 
suggestion of G. R. Robinson, we prove a block-theoretic analogue
of this theorem.