C4xC2 - Revision history

Charles Eaton: Added lifting column

2018-09-15T08:08:28Z

Added lifting column

Charles Eaton at 15:08, 8 September 2018

2018-09-08T15:08:03Z

Charles Eaton at 15:07, 8 September 2018

2018-09-08T15:07:11Z

Charles Eaton: Created page with "== Blocks with defect group $C_4 \times C_2$ == ${\rm Aut}(C_4 \times C_2)$ is an abelian $2$ -group and so every block with this defect group..."

2018-08-28T12:47:30Z

Created page with "== Blocks with defect group <math>C_4 \times C_2</math> == <math>{\rm Aut}(C_4 \times C_2)</math> is an abelian <math>2</math>-group and so every block with this defect group..."

New page

== Blocks with defect group <math>C_4 \times C_2</math> ==

<math>{\rm Aut}(C_4 \times C_2)</math> is an abelian <math>2</math>-group and so every block with this defect group is [[Nilpotent blocks|nilpotent]].

There is a unique <math>\mathcal{O}</math>-Morita equivalence class.

{| class="wikitable"
|-
! scope="col"| Class
! scope="col"| Representative
! 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

|-
|<math>M(8,2,1)</math> || <math>k(C_4 \times C_2)</math> ||8 ||1 ||<math>1</math> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 ||
|}

@@ Line 21: / Line 21: @@
 |-
-|M(8,2,1) || <math>k(C_4 \times C_2)</math> ||8 ||1 ||<math>1</math> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 ||
+|[[M(8,2,1)]] || <math>k(C_4 \times C_2)</math> ||8 ||1 ||<math>1</math> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 ||
 |}

@@ Line 1: / Line 1: @@
 == Blocks with defect group <math>C_4 \times C_2</math> ==
@@ Line 19: / Line 21: @@
 |-
-|<math>M(8,2,1)</math> || <math>k(C_4 \times C_2)</math> ||8 ||1 ||<math>1</math> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 ||
+|M(8,2,1) || <math>k(C_4 \times C_2)</math> ||8 ||1 ||<math>1</math> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 ||
 |}

@@ Line 3: / Line 3: @@
 == Blocks with defect group <math>C_4 \times C_2</math> ==
-<math>{\rm Aut}(C_4 \times C_2)</math> is an abelian <math>2</math>-group and so every block with this defect group is [[Nilpotent blocks|nilpotent]].
+<math>{\rm Aut}(C_4 \times C_2)</math> is a <math>2</math>-group and so every block with this defect group is [[Nilpotent blocks|nilpotent]].
 {| class="wikitable"
@@ Line 11: / Line 9: @@
 ! scope="col"| Class
 ! scope="col"| Representative
 ! scope="col"| <math>k(B)</math>
 ! scope="col"| <math>l(B)</math>
@@ Line 21: / Line 20: @@
 |-
-|[[M(8,2,1)]] || <math>k(C_4 \times C_2)</math> ||8 ||1 ||<math>1</math> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 ||
+|[[M(8,2,1)]] || <math>k(C_4 \times C_2)</math> || 1 ||8 ||1 ||<math>1</math> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 ||
 |}

C4xC2 - Revision history

Charles Eaton: Added lifting column

Charles Eaton at 15:08, 8 September 2018

Charles Eaton at 15:07, 8 September 2018

Charles Eaton: Created page with "== Blocks with defect group C_4 \times C_2 == {\rm Aut}(C_4 \times C_2) is an abelian 2-group and so every block with this defect group..."

Charles Eaton: Created page with "== Blocks with defect group $C_4 \times C_2$ == ${\rm Aut}(C_4 \times C_2)$ is an abelian $2$ -group and so every block with this defect group..."