Charles Eaton at 14:34, 12 April 2019

2019-04-12T14:34:52Z

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_8:C_4$ == $C_8:C_4$ is a metacyclic group of nonmaximal class, and so by Refe..."

2019-01-28T16:03:10Z

Created page with "__NOTITLE__ == Blocks with defect group <math>C_8:C_4</math> == <math>C_8:C_4</math> is a metacyclic group of nonmaximal class, and so by Refe..."

New page

__NOTITLE__

== Blocks with defect group <math>C_8:C_4</math> ==

<math>C_8:C_4</math> is a [[Metacyclic defect groups|metacyclic group]] of nonmaximal class, and so by [[References#C|[CG12]] or [[References#S|[Sa12b]]] there is only one possible [[Glossary#Fusion system|fusion system]]. Hence every block with this defect group is nilpotent.

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

{| 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(32,4,1)]] || <math>k(C_8:C_4)</math> || 1 ||20 (16,4) ||1 ||<math>1</math> || || ||1 ||1 ||
|}

@@ Line 3: / Line 3: @@
 == Blocks with defect group <math>C_8:C_4</math> ==
-<math>C_8:C_4</math> is a [[Metacyclic defect groups|metacyclic group]] of nonmaximal class, and so by [[References#C|[CG12]] or [[References#S|[Sa12b]]] there is only one possible [[Glossary#Fusion system|fusion system]]. Hence every block with this defect group is nilpotent.
+<math>C_8:C_4</math> is a [[Metacyclic defect groups|metacyclic group]] of nonmaximal class, and so by [[References#C|[CG12]]] or [[References#S|[Sa12b]]] there is only one possible [[Glossary#Fusion system|fusion system]]. Hence every block with this defect group is nilpotent.
 There is a unique <math>\mathcal{O}</math>-Morita equivalence class.

C8:C4 - Revision history

Charles Eaton at 14:34, 12 April 2019

Charles Eaton: Created page with "__NOTITLE__ == Blocks with defect group C_8:C_4 == C_8:C_4 is a metacyclic group of nonmaximal class, and so by Refe..."

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_8:C_4$ == $C_8:C_4$ is a metacyclic group of nonmaximal class, and so by Refe..."