Charles Eaton at 07:14, 4 June 2019

2019-06-04T07:14:42Z

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_{2^m} \times C_{2^m}$ for $m>1$ == These blocks were classified them over $\mathcal{O}$ in Refe..."

2018-11-23T09:28:30Z

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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__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 [[References|[EKKS14]]] using the [[Glossary|CFSG]]. The Picard groups with respect to <math>\mathcal{O}</math> follow from [[References|[BKL18]]].

{| class="wikitable"
|-
! scope="col"| Class
! scope="col"| Representative
! scope="col"| # lifts / <math>\mathcal{O}</math>
! scope="col"| <math>k(B)</math>
! scope="col"| <math>l(B)</math>
! scope="col"| Inertial quotients
! scope="col"| <math>{\rm Pic}_\mathcal{O}(B)</math>
! scope="col"| <math>{\rm Pic}_k(B)</math>
! scope="col"| <math>{\rm mf_\mathcal{O}(B)}</math>
! scope="col"| <math>{\rm mf_k(B)}</math>
! scope="col"| Notes

|-
|[[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 ||
|-
|[[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 ||
|}

@@ 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-1}} \times S_3)</math> || ||1 ||1 ||
+|[[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> ||<math>S_3 \times C_{2^{m-1}}</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> || || ||1 ||1 ||
 |}

C(2^m)xC(2^m) - Revision history

Charles Eaton at 07:14, 4 June 2019

Charles Eaton: Created page with "__NOTITLE__ == Blocks with defect group C_{2^m} \times C_{2^m} for m>1 == These blocks were classified them over \mathcal{O} in Refe..."

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_{2^m} \times C_{2^m}$ for $m>1$ == These blocks were classified them over $\mathcal{O}$ in Refe..."