Difference between revisions of "C4xC2"

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== Blocks with defect group <math>C_4 \times C_2</math> ==
 
== Blocks with defect group <math>C_4 \times C_2</math> ==
  
<math>{\rm Aut}(C_4 \times C_2)</math> is an abelian <math>2</math>-group and so every block with this defect group is [[Nilpotent blocks|nilpotent]].
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<math>{\rm Aut}(C_4 \times C_2)</math> is a <math>2</math>-group and so every block with this defect group is [[Nilpotent blocks|nilpotent]].  
 
 
There is a unique <math>\mathcal{O}</math>-Morita equivalence class.
 
  
 
{| class="wikitable"
 
{| class="wikitable"
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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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|-
 
|-
|M(8,2,1) || <math>k(C_4 \times C_2)</math> ||8 ||1 ||<math>1</math> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 ||  
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|[[M(8,2,1)]] || <math>k(C_4 \times C_2)</math> || 1 ||8 ||1 ||<math>1</math> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 ||  
 
|}
 
|}

Latest revision as of 08:08, 15 September 2018

Blocks with defect group [math]C_4 \times C_2[/math]

[math]{\rm Aut}(C_4 \times C_2)[/math] is a [math]2[/math]-group and so every block with this defect group is nilpotent.

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(8,2,1) [math]k(C_4 \times C_2)[/math] 1 8 1 [math]1[/math] [math](C_4 \times C_2):(C_2 \times C_2 \times C_2)[/math] 1 1