Difference between revisions of "C4xC4"

From Block library
Jump to: navigation, search
(Created page with "__NOTITLE__ == 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...")
 
(Corrected Picard group)
Line 22: Line 22:
 
|[[M(16,2,1)]] || <math>k(C_4 \times C_4)</math> || 1 ||16 ||1 ||<math>1</math> ||<math>(C_4 \times C_4):S_3</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):S_3</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>S_3</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 ||  
 
|}
 
|}

Revision as of 13:16, 14 November 2018

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 isomorphic to [math]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):S_3[/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