Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_{32}$ == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a uniq..."

2019-01-28T15:34:16Z

Created page with "__NOTITLE__ == Blocks with defect group <math>C_{32}</math> == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a uniq..."

New page

__NOTITLE__

== Blocks with defect group <math>C_{32}</math> ==

These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].

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(32,1,1)]] || <math>kC_{32}</math> || 1 ||32 ||1 ||<math>1</math> ||<math>C_{32}:(C_8 \times C_2)</math> || <math>k^{30}:k^*</math> ||1 ||1 ||
|}

[[Category:Cyclic p-group]]
[[Category: p-group]]

C32 - Revision history

Charles Eaton: Created page with "__NOTITLE__ == Blocks with defect group C_{32} == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a uniq..."

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_{32}$ == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a uniq..."