The structure of blocks with a Klein four defect group

Abstract

We prove Erdmann's conjecture (J Algebra 76:505-518, 1982) stating that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig's finiteness conjecture holds for source algebras of blocks with a Klein four defect group. The proof uses the classification of finite simple groups. © 2010 Springer-Verlag.