Difference between revisions of "C(2^m)xC(2^m)"
(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...") |
|||
| Line 20: | Line 20: | ||
|- | |- | ||
| − | |[[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(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 || |
|- | |- | ||
| − | |[[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> || | + | |[[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 || |
|} | |} | ||
Latest revision as of 08:14, 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 |
