Difference between revisions of "C2"

Revision as of 08:00, 15 September 2018

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	Representative	# lifts / [math]\mathcal{O}[/math]	[math]k(B)[/math]	[math]l(B)[/math]	Inertial quotients	[math]{\rm Pic}_\mathcal{O}(B)[/math]	[math]{\rm Pic}_k(B)[/math]	[math]{\rm mf_\mathcal{O}(B)}[/math]	[math]{\rm mf_k(B)}[/math]	Notes
M(2,1,1)	[math]kC_2[/math]	1	2	1	[math]1[/math]	[math]C_2[/math]	[math]k[/math]	1	1

@@ Line 11: / Line 11: @@
 ! 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>
@@ Line 21: / Line 22: @@
 |-
-|[[M(2,1,1)]] || <math>kC_2</math> ||2 ||1 ||<math>1</math> ||<math>C_2</math> ||<math>k</math> ||1 ||1 ||
+|[[M(2,1,1)]] || <math>kC_2</math> || 1 ||2 ||1 ||<math>1</math> ||<math>C_2</math> ||<math>k</math> ||1 ||1 ||
 |}
 [[Category:Cyclic p-group]]
 [[Category: p-group]]