Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_{2^n}$ == ${\rm Aut}(C_{2^n})$ is a 2-group for all $n$ , hence every block with such a defect gro..."

2018-09-08T14:57:41Z

Created page with "__NOTITLE__ == Blocks with defect group <math>C_{2^n}</math> == <math>{\rm Aut}(C_{2^n})</math> is a 2-group for all <math>n</math>, hence every block with such a defect gro..."

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__NOTITLE__

== Blocks with defect group <math>C_{2^n}</math> ==

<math>{\rm Aut}(C_{2^n})</math> is a 2-group for all <math>n</math>, hence every block with such a defect group is nilpotent.

{| 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

|-
|[[M(2^n,1,1)|M(<math>2^n</math>,1,1)]] || <math>kC_{2^n}</math> || <math>2^n</math> ||1 ||<math>1</math> ||<math>C_{2^n} : C_{2^{n-1}}</math> || ||1 ||1 ||
|}

C(2^n) - Revision history

Charles Eaton: Created page with "__NOTITLE__ == Blocks with defect group C_{2^n} == {\rm Aut}(C_{2^n}) is a 2-group for all n, hence every block with such a defect gro..."

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_{2^n}$ == ${\rm Aut}(C_{2^n})$ is a 2-group for all $n$ , hence every block with such a defect gro..."