TWISTED GROUP ALGEBRAS, NORMAL SUBGROUPS AND DERIVED EQUIVALENCES
Andrei Marcus
Preprint April 13, 2000

http://www.minet.uni-jena.de/~amarcus/

Abstract. We study Rickard equivalences between $p$-blocks of twisted group
algebras and their local structure, in connection with Dade's conjectures.
We prove that an extended form of Brou\'e's conjecture implies Dade's
Inductive Conjecture in the abelian defect group case; this is a consequence
of the fact that Rickard equivalences induced by complexes of graded
bimodules preserve the relevant Clifford theoretical invariants.
As an application, we show that these conjectures hold for $p'$-extensions 
of blocks with with cyclic defect  groups.