Difference between revisions of "C2"

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(Created page with " == Blocks with defect group <math>C_2</math> == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a unique <math>\mathc...")
 
 
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__NOTITLE__
  
 
== Blocks with defect group <math>C_2</math> ==
 
== Blocks with defect group <math>C_2</math> ==
  
These are blocks with [[cyclic defect groups]] and so they are described by [[Brauer trees]].
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These are blocks with [[Blocks with cyclic defect groups|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(2,1,1)</math>
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|[[M(2,1,1)]] || <math>kC_2</math> || 1 ||2 ||1 ||<math>1</math> ||<math>C_2</math> ||<math>k^*</math> ||1 ||1 ||
|<math>kC_2</math>
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|}
|2
 
|1
 
|<math>1</math>
 
|<math>C_2</math>
 
|<math>k</math>
 
|1
 
|1
 
  
|}
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[[Category:Cyclic p-group]]
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[[Category: p-group]]

Latest revision as of 21:59, 21 November 2018

Blocks with defect group [math]C_2[/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(2,1,1) [math]kC_2[/math] 1 2 1 [math]1[/math] [math]C_2[/math] [math]k^*[/math] 1 1