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| − | <div style="font-size: | + | <div style="font-size:170%; font-weight:bold; padding:.1em;">Blocks of finite groups</div> |
<div style="font-size:95%;">Donovan's conjecture and the classification </div> | <div style="font-size:95%;">Donovan's conjecture and the classification </div> | ||
<div style="font-size:95%;">of Morita equivalence classes</div> | <div style="font-size:95%;">of Morita equivalence classes</div> | ||
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<li style="position:absolute; left:0; top:0;">[[Status of Donovan's conjecture]]</li> | <li style="position:absolute; left:0; top:0;">[[Status of Donovan's conjecture]]</li> | ||
<li style="position:absolute; left:0; top:1.6em;">[[Classification by p-group]]</li> | <li style="position:absolute; left:0; top:1.6em;">[[Classification by p-group]]</li> | ||
<li style="position:absolute; left:0; top:3.2em;">[[Generic classifications by p-group class]]</li> | <li style="position:absolute; left:0; top:3.2em;">[[Generic classifications by p-group class]]</li> | ||
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| + | A resource for progress on [[Statements_of_conjectures#Donovan's conjecture|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 [[User:Charles Eaton|Charles Eaton]]. A more detailed account of the purpose and content of the site can be found [[About the site|here]]. | ||
| − | + | In October 2026 OpenAI released a claimed proof of Donovan's conjecture, with different manuscripts for <math>k</math> ([[References#O|[OpenAI26a]]]) and <math>\mathcal{O}</math> ([[References#O|[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!). | |
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| − | + | | style="width:50%; border:1px solid #a3e4d7; padding:0; background:#f5fffa; vertical-align:top; color:#000;" | | |
| + | <h2 style="margin:0.5em; background:#cef2e0; font-family:inherit; font-size:120%; font-weight:bold; border:1px solid #a3bfb1; color:#000; padding:0.2em 0.4em;">Classifications</h2> | ||
*[[Classification by p-group]] | *[[Classification by p-group]] | ||
*[[Generic classifications by p-group class]] | *[[Generic classifications by p-group class]] | ||
| − | *[[Open problems| | + | *[[Results on classes of groups]] |
| + | *[[Miscallaneous results]] | ||
| + | *[[Fusion-trivial p-groups]] | ||
| + | *[[Open problems]] | ||
| + | <div style="padding:0.1em 0.6em;"></div> | ||
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| + | | style="border:1px solid transparent;" | | ||
| + | | style="width:50%; border:1px solid #aed6f1; padding:0; background:#f5faff; vertical-align:top;"| | ||
| + | <h2 style="margin:0.5em; background:#cedff2; font-family:inherit; font-size:120%; font-weight:bold; border:1px solid #a3b0bf; color:#000; padding:0.2em 0.4em;">Conjectures</h2> | ||
| + | *[[Statements of conjectures]] | ||
| + | *[[Status of Donovan's conjecture]] | ||
*[[Reductions]] | *[[Reductions]] | ||
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| + | |} | ||
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| + | | style="width:50%; border:1px solid #d6b8b8; ; padding:0; background:#fff9f9; vertical-align:top; color:#000;" | | ||
| + | <h2 id="mp-tfa-h2" style="margin:0.5em; background:#f9e8e8; font-family:inherit; font-size:120%; font-weight:bold; border:1px solid #b59898; color:#000; padding:0.2em 0.4em;">Resources</h2> | ||
| + | *[[Background and conjectures]] | ||
*[[Notation]] | *[[Notation]] | ||
| + | *[[Labelling for Morita equivalence classes]] | ||
| + | *[[Glossary]] | ||
*[[References]] | *[[References]] | ||
| + | *[[Other resources|Links to other resources]] | ||
*[[Guide to Contributing]] | *[[Guide to Contributing]] | ||
| + | *[[To do list]] | ||
| + | <div style="padding:0.1em 0.6em;"></div> | ||
| + | |||
| + | | style="border:1px solid transparent;" | | ||
| + | | style="width:50%; border:1px solid #d7bde2; padding:0; background:#f5eef8; vertical-align:top;"| | ||
| + | <h2 style="margin:0.5em; background: #ebdef0; font-family:inherit; font-size:120%; font-weight:bold; border:1px solid #c39bd3; color:#000; padding:0.2em 0.4em;">Picard groups</h2> | ||
| + | *[[Picard groups]] | ||
| + | *[[Known Picard groups]] | ||
| + | *[[Groups of perfect self-isometries]] | ||
| + | <div style="padding:0.1em 0.6em;"></div> | ||
| + | |} | ||
| + | |||
| + | This wiki site was set up by [[User:Charles Eaton|Charles Eaton]] and [[User:CesareGArdito|Cesare G. Ardito]] and is maintained by [[User:Charles Eaton|Charles Eaton]] and hosted at the University of Manchester. | ||
Latest revision as of 11:31, 8 October 2026
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 |
Conjectures |
Resources |
Picard groups |
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.
