Difference between revisions of "C4:C4"

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(Created page with "__NOTITLE__ == Blocks with defect group <math>C_4:C_4</math> == <math>C_4:C_4</math> is a metacyclic group of nonmaximal class, and so by Refe...")
 
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|[[M(16,4,1)]] || <math>k(C_4:C_4)</math> || 1 ||10 ||1 ||<math>1</math> ||<math>(C_4 \times C_4):{\rm Aut}(C_4:C_4)</math> || ||1 ||1 ||  
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|[[M(16,4,1)]] || <math>k(C_4:C_4)</math> || 1 ||10 ||1 ||<math>1</math> || || ||1 ||1 ||  
 
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Revision as of 07:51, 5 October 2018

Blocks with defect group [math]C_4:C_4[/math]

[math]C_4:C_4[/math] is a metacyclic group of nonmaximal class, and so by [Sa12b] there is only one possible fusion system. Hence every block with this defect group is nilpotent.

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(16,4,1) [math]k(C_4:C_4)[/math] 1 10 1 [math]1[/math] 1 1