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Blocks of finite groups

Donovan's conjecture and the classification

of Morita equivalence classes

A resource for progress on Donovan's conjecture and for the classification of Morita equivalence classes of blocks with a given defect group. The intention is to eventually make the site editable by all, but at the moment it is in its early stages. If you would like to contribute to this site, then please contact Charles Eaton. A more detailed account of the purpose and content of the site can be found here.

In October 2026 OpenAI released a claimed proof of Donovan's conjecture, with different manuscripts for [math]k[/math] ([OpenAI26a]) and [math]\mathcal{O}[/math] ([OpenAI26b]), using the classification of finite simple groups. As of 8/10/2026 we are still attempting to check/understand the proof, and this is likely to take some time (especially since we are simultaneously interested in the claimed proof of Alperin's weight conjecture!).

Classifications Classification by p-group Generic classifications by p-group class Results on classes of groups Miscallaneous results Fusion-trivial p-groups Open problems

Conjectures Statements of conjectures Status of Donovan's conjecture Reductions

Resources Background and conjectures Notation Labelling for Morita equivalence classes Glossary References Links to other resources Guide to Contributing To do list

Picard groups Picard groups Known Picard groups Groups of perfect self-isometries

This wiki site was set up by Charles Eaton and Cesare G. Ardito and is maintained by Charles Eaton and hosted at the University of Manchester.