72 research outputs found
On blocks with trivial source simple modules
Motivated by an observation in "Vertices, sources and Green correspondents of
the simple modules for the large Mathieu groups", J. of Algebra 322, we
determine the source algebra, and therefore all the structure, of the blocks
without essential Brauer pairs where the simple modules of all the Brauer
corespondents have trivial sources
Glauberman correspondents and extensions of nilpotent block algebras
The main purpose of this paper is to prove that the extensions of a nilpotent
block algebra and its Glauberman correspondent block algebra are Morita
equivalent under an additional group-theoretic condition. In particular, Harris
and Linckelman's theorem and Koshitani and Michler's theorem are covered. The
ingredient to carry out our purpose is the two main results in K\"ulshammer and
Puig's work "Extensions of nilpotent blocks"; we actually revisited them,
giving completely new proofs of both and slightly improving the second one
- …