Shigeo Koshitani and Naoko Kunugi

Broue conjecture holds for principal 3-blocks with elementary abelian 
defect group of order 9

Abstract. In representation theory of finite groups, there is a well known
and important conjecture due to M. Brou\'e. He has conjectured that, for
any prime $p$, if a finite group $G$ has an abelian Sylow $p$-subgroup $P$,
then the principal $p$-blocks of $G$ and of the normalizer $N_G(P)$ of $P$
in $G$ are derived equivalent. We prove in this paper that the Brou\'e 
conjecture holds for the principal 3-block of an arbitrary finite group $G$
with elementary abelian Sylow 3-subgroup $P$ of order 9, by using initiated
works for the case that $G$ is simple, which are due to Puig, Okuyama, Waki,
Miyachi and the authors. The result depends on the classification of finite
simple groups.