Difference between revisions of "C(2^m)xC(2^m)"

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(Created page with "__NOTITLE__ == Blocks with defect group <math>C_{2^m} \times C_{2^m}</math> for <math>m>1</math> == These blocks were classified them over <math>\mathcal{O}</math> in Refe...")
 
 
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|[[M(2^mx2^m,1)|M(<math>C_{2^m} \times C_{2^m}</math>,1)]] || <math>k(C_{2^m} \times C_{2^m})</math> || 1 || <math>2^{2m}</math> ||1 ||<math>1</math> ||<math>(C_{2^m} \times C_{2^m}):(C_{2^{m-1}} \times S_3)</math> || ||1 ||1 ||
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|[[M(2^mx2^m,1)|M(<math>C_{2^m} \times C_{2^m}</math>,1)]] || <math>k(C_{2^m} \times C_{2^m})</math> || 1 || <math>2^{2m}</math> ||1 ||<math>1</math> ||<math>(C_{2^m} \times C_{2^m}):Aut(C_{2^m} \times C_{2^m})</math> || ||1 ||1 ||
 
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|[[M(2^mx2^m,2)|M(<math>C_{2^m} \times C_{2^m}</math>,2)]] || <math>k(C_{2^m} \times C_{2^m}):C_3</math> || 1 || <math>(2^{2m}+8)/3</math> ||3 ||<math>C_3</math> ||<math>S_3 \times C_{2^{m-1}}</math> || ||1 ||1 ||
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|[[M(2^mx2^m,2)|M(<math>C_{2^m} \times C_{2^m}</math>,2)]] || <math>k(C_{2^m} \times C_{2^m}):C_3</math> || 1 || <math>(2^{2m}+8)/3</math> ||3 ||<math>C_3</math> || || ||1 ||1 ||
 
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Latest revision as of 07:14, 4 June 2019

Blocks with defect group [math]C_{2^m} \times C_{2^m}[/math] for [math]m\gt 1[/math]

These blocks were classified them over [math]\mathcal{O}[/math] in [EKKS14] using the CFSG. The Picard groups with respect to [math]\mathcal{O}[/math] follow from [BKL18].

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([math]C_{2^m} \times C_{2^m}[/math],1) [math]k(C_{2^m} \times C_{2^m})[/math] 1 [math]2^{2m}[/math] 1 [math]1[/math] [math](C_{2^m} \times C_{2^m}):Aut(C_{2^m} \times C_{2^m})[/math] 1 1
M([math]C_{2^m} \times C_{2^m}[/math],2) [math]k(C_{2^m} \times C_{2^m}):C_3[/math] 1 [math](2^{2m}+8)/3[/math] 3 [math]C_3[/math] 1 1