# A note on vertices of indecomposable tensor products

## TL;DR

This paper provides a sufficient criterion for when the vertices of two indecomposable modules over a finite group algebra generate a Sylow p-subgroup, extending Navarro's earlier result for simple modules.

## Contribution

It generalizes Navarro's result by establishing a criterion applicable to indecomposable modules beyond simple modules over finite p-solvable groups.

## Key findings

- Provides a sufficient condition for vertices to generate a Sylow p-subgroup
- Extends Navarro's result to a broader class of modules
- Offers insights into the structure of indecomposable modules

## 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.