Difference between revisions of "C4xC4"

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(Blocks with defect group C_4 \times C_4)
(Blocks with defect group C_4 \times C_4)
 
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== Blocks with defect group <math>C_4 \times C_4</math> ==
 
== Blocks with defect group <math>C_4 \times C_4</math> ==
  
These are blocks were first classified over <math>\mathcal{O}</math> in [[References|[EKKS14]]] using the [[Glossary#CFSG|CFSG]]. Each <math>k</math>-Morita equivalence class lifts to an unique <math>\mathcal{O}</math>-Morita equivalence class. The automorphism group of <math>C_4 \times C_4</math> is isomorphic to <math>S_3</math>.
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These are blocks were first classified over <math>\mathcal{O}</math> in [[References|[EKKS14]]] using the [[Glossary#CFSG|CFSG]]. Each <math>k</math>-Morita equivalence class lifts to an unique <math>\mathcal{O}</math>-Morita equivalence class. The automorphism group of <math>C_4 \times C_4</math> is SmallGroup(96,195), which has isomorphism type <math>(C_2)^4:S_3</math>.
  
 
{| class="wikitable"
 
{| class="wikitable"
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|[[M(16,2,1)]] || <math>k(C_4 \times C_4)</math> || 1 ||16 ||1 ||<math>1</math> ||<math>(C_4 \times C_4):({\rm Aut}(C_4 \times C_4))</math> || ||1 ||1 ||
 
|[[M(16,2,1)]] || <math>k(C_4 \times C_4)</math> || 1 ||16 ||1 ||<math>1</math> ||<math>(C_4 \times C_4):({\rm Aut}(C_4 \times C_4))</math> || ||1 ||1 ||
 
|-
 
|-
|[[M(16,2,2)]] || <math>k((C_4 \times C_4):C_3)</math> || 1 ||8 ||3 ||<math>C_3</math> ||<math>C_2 \times S_3</math> || ||1 ||1 ||  
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|[[M(16,2,2)]] || <math>k((C_4 \times C_4):C_3)</math> || 1 ||8 ||3 ||<math>C_3</math> || || ||1 ||1 ||  
 
|}
 
|}

Latest revision as of 07:13, 4 June 2019

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

These are blocks were first classified over [math]\mathcal{O}[/math] in [EKKS14] using the CFSG. Each [math]k[/math]-Morita equivalence class lifts to an unique [math]\mathcal{O}[/math]-Morita equivalence class. The automorphism group of [math]C_4 \times C_4[/math] is SmallGroup(96,195), which has isomorphism type [math](C_2)^4:S_3[/math].

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(16,2,1) [math]k(C_4 \times C_4)[/math] 1 16 1 [math]1[/math] [math](C_4 \times C_4):({\rm Aut}(C_4 \times C_4))[/math] 1 1
M(16,2,2) [math]k((C_4 \times C_4):C_3)[/math] 1 8 3 [math]C_3[/math] 1 1