# Open problems

This page is for open problems, large and small, relating to module categories for blocks. Missing data is also flagged within tables elsewhere on this site.

## Contents

## General problems

- Is the isomorphism type of the defect group a Morita invariant?
- Is [math]{\rm Pic}_\mathcal{O}(B)[/math] always finite?
- Is every Morita equivalence between [math]\mathcal{O}[/math]-blocks endopermutation source?

## Open cases for classifications of Morita equivalence classes for a given [math]p[/math]-group

- Which Brauer trees give rise to blocks with defect group [math]C_7[/math]? (This is the smallest cyclic group for which the classification is not known).

## Picard groups

## Basic algebras of dimension 9

Does the 9-dimensional algebra described in Blocks with basic algebras of low dimension occur as the basic algebra of a block of a finite group?