Vertices of simple modules

Burkhard Külshammer, University of Jena

Every indecomposable module M of a finite group G over a field F of characteristic p > 0 determines a conjugacy class of p-subgroups Q of G, called the vertices of M. When M is simple then, by a theorem of Knörr, Q contains the center of a defect group of the block of G defined by M. There are a number of open questions on vertices of simple modules in the literature. In the talk we will answer some of them, correct a mistake and prove some new results.