MNA(2,2) - Revision history

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $MNA(2,2)=\langle x,y|x^4=y^4=[x,y]^2=[x,[x,y]]=[y,[x,y]]=1 \rangle$ == The defect groups are minimal nonabelian $2$
2019-01-28T15:46:35Z

Created page with "NOTITLE == Blocks with defect group <math>MNA(2,2)=\langle x,y|x^4=y^4=[x,y]^2=[x,[x,y]]=[y,[x,y]]=1 \rangle</math> == The defect groups are minimal nonabelian <math>2</..."

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== Blocks with defect group <math>MNA(2,2)=\langle x,y|x^4=y^4=[x,y]^2=[x,[x,y]]=[y,[x,y]]=1 \rangle</math> ==

The defect groups are minimal nonabelian <math>2</math>-groups. The <math>\mathcal{O}</math>-Morita equivalence classes are classified in [[References#E|[EKS12]]].

{| 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(32,2,1)]] || <math>k(MNA(2,2))</math> || 1 ||20 (16,4) ||1 ||<math>1</math> || || ||1 ||1 ||
|-
|[[M(32,2,2)]] || <math>k(MNA(2,2):C_3)</math> || 1 ||12 (8,4) ||3 ||<math>C_3</math> || || ||1 ||1 ||
|}