Difference between revisions of "C16"
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== Blocks with defect group <math>C_{16}</math> == | == Blocks with defect group <math>C_{16}</math> == | ||
| − | These are blocks with | + | These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]]. |
There is a unique <math>\mathcal{O}</math>-Morita equivalence class. | There is a unique <math>\mathcal{O}</math>-Morita equivalence class. | ||
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| − | |[[M(16,1,1)]] || <math>kC_{16}</math> || 1 ||16 ||1 ||<math>1</math> ||<math>C_{16}:(C_4 \times C_2)</math> || ||1 ||1 || | + | |[[M(16,1,1)]] || <math>kC_{16}</math> || 1 ||16 ||1 ||<math>1</math> ||<math>C_{16}:(C_4 \times C_2)</math> || <math>k^{14}:k^*</math> ||1 ||1 || |
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| + | [[Category:Cyclic p-group]] | ||
| + | [[Category: p-group]] | ||
Latest revision as of 11:19, 22 November 2018
Blocks with defect group [math]C_{16}[/math]
These are blocks with cyclic defect groups and so they are described by Brauer trees.
There is a unique [math]\mathcal{O}[/math]-Morita equivalence class.
| Class | Representative | # lifts / [math]\mathcal{O}[/math] | [math]k(B)[/math] | [math]l(B)[/math] | Inertial quotients | [math]{\rm Pic}_\mathcal{O}(B)[/math] | [math]{\rm Pic}_k(B)[/math] | [math]{\rm mf_\mathcal{O}(B)}[/math] | [math]{\rm mf_k(B)}[/math] | Notes |
|---|---|---|---|---|---|---|---|---|---|---|
| M(16,1,1) | [math]kC_{16}[/math] | 1 | 16 | 1 | [math]1[/math] | [math]C_{16}:(C_4 \times C_2)[/math] | [math]k^{14}:k^*[/math] | 1 | 1 |
