C4xC4 - Revision history

Charles Eaton: /* Blocks with defect group C_4 \times C_4 */

2019-06-04T07:13:07Z

‎Blocks with defect group C_4 \times C_4

Charles Eaton at 11:59, 15 November 2018

2018-11-15T11:59:07Z

Charles Eaton: /* Blocks with defect group C_4 \times C_4 */

2018-11-15T09:49:45Z

‎Blocks with defect group C_4 \times C_4

Charles Eaton at 13:18, 14 November 2018

2018-11-14T13:18:14Z

Charles Eaton: Corrected Picard group

2018-11-14T13:16:43Z

Corrected Picard group

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_4 \times C_4$ == These are blocks were first classified over $\mathcal{O}$ in [EKKS14] using..."

2018-10-03T20:11:57Z

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..."

New page

__NOTITLE__

== Blocks with defect group <math>C_4 \times C_4</math> ==

These are blocks were first classified over <math>\mathcal{O}</math> in [[References|[EKKS14]]] using the [[Glossary#CFSG|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="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(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 ||
|}

@@ 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):({\rm Aut}(C_4 \times C_4))</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 ||
+|[[M(16,2,2)]] || <math>k((C_4 \times C_4):C_3)</math> || 1 ||8 ||3 ||<math>C_3</math> || || ||1 ||1 ||
 |}

@@ Line 20: / Line 20: @@
 |-
-|[[M(16,2,1)]] || <math>k(C_4 \times C_4)</math> || 1 ||16 ||1 ||<math>1</math> ||<math>(C_4 \times C_4):(C_2 \times 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):({\rm Aut}(C_4 \times C_4))</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 ||
 |}

@@ Line 20: / Line 20: @@
 |-
-|[[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):(C_2 \times 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 ||
 |}

@@ Line 3: / Line 3: @@
 == Blocks with defect group <math>C_4 \times C_4</math> ==
-These are blocks were first classified over <math>\mathcal{O}</math> in [[References|[EKKS14]]] using the [[Glossary#CFSG|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>.
+These are blocks were first classified over <math>\mathcal{O}</math> in [[References|[EKKS14]]] using the [[Glossary#CFSG|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 SmallGroup(96,195), which has isomorphism type <math>(C_2)^4:S_3</math>.
 {| class="wikitable"

C4xC4 - Revision history

Charles Eaton: /* Blocks with defect group C_4 \times C_4 */

Charles Eaton at 11:59, 15 November 2018

Charles Eaton: /* Blocks with defect group C_4 \times C_4 */

Charles Eaton at 13:18, 14 November 2018

Charles Eaton: Corrected Picard group

Charles Eaton: Created page with "__NOTITLE__ == Blocks with defect group C_4 \times C_4 == These are blocks were first classified over \mathcal{O} in [EKKS14] using..."

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_4 \times C_4$ == These are blocks were first classified over $\mathcal{O}$ in [EKKS14] using..."