Difference between revisions of "C8"

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__NOTITLE__
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== Blocks with defect group <math>C_8</math> ==
 
== Blocks with defect group <math>C_8</math> ==
  
These are blocks with [[cyclic defect groups]] and so they are described by [[Brauer trees]].
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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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! scope="col"| Class
 
! scope="col"| Class
 
! scope="col"| Representative
 
! scope="col"| Representative
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! scope="col"| # lifts / <math>\mathcal{O}</math>
 
! scope="col"| <math>k(B)</math>
 
! scope="col"| <math>k(B)</math>
 
! scope="col"| <math>l(B)</math>
 
! scope="col"| <math>l(B)</math>
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|<math>M(8,1,1)</math> || <math>kC_8</math> ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C2)</math> || ||1 ||1 ||  
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|[[M(8,1,1)]] || <math>kC_8</math> || 1 ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C_2)</math> || <math>k^6:k^*</math> ||1 ||1 ||  
 
|}
 
|}
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[[Category:Cyclic p-group]]
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[[Category: p-group]]

Latest revision as of 10:19, 22 November 2018

Blocks with defect group [math]C_8[/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(8,1,1) [math]kC_8[/math] 1 8 1 [math]1[/math] [math]C_8:(C_2 \times C_2)[/math] [math]k^6:k^*[/math] 1 1