Charles Eaton at 15:02, 12 April 2019

2019-04-12T15:02:54Z

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $MNA(3,1):C_2=\langle a,b,c,d | a^2=b^2=c^2=d^4=1, ab=ba, ac=ca, dad^{-1}=abc, dbd^{-1}=bc=cb, cd=dc \rangle$ == Sambale h..."

2019-04-12T14:58:33Z

Created page with "__NOTITLE__ == Blocks with defect group <math>MNA(3,1):C_2=\langle a,b,c,d | a^2=b^2=c^2=d^4=1, ab=ba, ac=ca, dad^{-1}=abc, dbd^{-1}=bc=cb, cd=dc \rangle</math> == Sambale h..."

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__NOTITLE__

== Blocks with defect group <math>MNA(3,1):C_2=\langle a,b,c,d | a^2=b^2=c^2=d^4=1, ab=ba, ac=ca, dad^{-1}=abc, dbd^{-1}=bc=cb, cd=dc \rangle</math> ==

Sambale has used GAP to show that there are no non-trivial saturated fusion systems on <math>MNA(3,1):C_2</math> (see [[References#S|[Sa14]]]). See also [[References#V|[vdW, pp. 382]]]. 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(MNA(3,1):C_2)</math> || 1 ||11 (8,2,1) ||1 ||<math>1</math> || || ||1 ||1 ||
|}

@@ Line 3: / Line 3: @@
 == Blocks with defect group <math>MNA(3,1):C_2=\langle a,b,c,d | a^2=b^2=c^2=d^4=1, ab=ba, ac=ca, dad^{-1}=abc, dbd^{-1}=bc=cb, cd=dc \rangle</math> ==
-Sambale has used GAP to show that there are no non-trivial saturated fusion systems on <math>MNA(3,1):C_2</math> (see [[References#S|[Sa14]]]). See also [[References#V|[vdW, pp. 382]]]. Hence every block with this defect group is nilpotent.
+Sambale has used GAP to show that there are no non-trivial saturated fusion systems on <math>MNA(3,1):C_2</math> (see [[References#S|[Sa14]]]). See also [[References#V|[vdW91, pp. 382]]]. Hence every block with this defect group is nilpotent.
 There is a unique <math>\mathcal{O}</math>-Morita equivalence class.

MNA(3,1):C2 - Revision history

Charles Eaton at 15:02, 12 April 2019

Charles Eaton: Created page with "__NOTITLE__ == Blocks with defect group MNA(3,1):C_2=\langle a,b,c,d | a^2=b^2=c^2=d^4=1, ab=ba, ac=ca, dad^{-1}=abc, dbd^{-1}=bc=cb, cd=dc \rangle == Sambale h..."

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $MNA(3,1):C_2=\langle a,b,c,d | a^2=b^2=c^2=d^4=1, ab=ba, ac=ca, dad^{-1}=abc, dbd^{-1}=bc=cb, cd=dc \rangle$ == Sambale h..."