A note on vertices of indecomposable tensor products

Abstract

G. Navarro raised the question under what circumstancs two vertices of two indecomposable modules over a finite group algebra generate a Sylow $p$-subgroup. The present note provides a sufficient criterion for when this is the case. This generalises a result by Navarro for simple modules over finite $p$-solvable groups, which is the main motivation for this note.