Charles Eaton at 11:21, 4 January 2019

2019-01-04T11:21:09Z

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $D_8 \times C_2$ == The invariants $k(B)$ , $k_i(B)$ and $l(B)$ are determined in Refere..."

2018-11-27T09:02:40Z

Created page with "__NOTITLE__ == Blocks with defect group <math>D_8 \times C_2</math> == The invariants <math>k(B)</math>, <math>k_i(B)</math> and <math>l(B)</math> are determined in Refere..."

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__NOTITLE__

== Blocks with defect group <math>D_8 \times C_2</math> ==

The invariants <math>k(B)</math>, <math>k_i(B)</math> and <math>l(B)</math> are determined in [[References|[Sa12]]]. There is as yet no classification of blocks with these defect groups, and Donovan's conjecture is not known in any form.

'''<pre style="color: red">CLASSIFICATION INCOMPLETE</pre>'''



== Notes ==

<references />

@@ Line 7: / Line 7: @@
 '''<pre style="color: red">CLASSIFICATION INCOMPLETE</pre>'''
-<!--{| class="wikitable"
+{| class="wikitable"
 |-
 ! scope="col"| Class
@@ Line 22: / Line 22: @@
 |-
-|[[M(16,9,1)]] || <math>kSD_{16}</math> || 1 ||7 ||1 ||<math>1</math> || || || ||1 ||
+|[[M(16,11,1)]] || <math>k(D_8 \times C_2)</math> || ? ||10 ||1 ||<math>1</math> || || || ||1 ||
 |-
-|[[M(16,9,2)]] || <math>B_0(k \tilde{S}_5)</math><ref>This is the double cover SmallGroup(240,89)</ref> || ? ||8 ||2 ||<math>1</math> || || || ||1 || <math>Q(2 {\cal A})</math>
+|[[M(16,11,2)]] || <math>B_0(k(PGL_2(5) \times C_2))</math> || ? ||10 ||2 ||<math>1</math> || || || ||1 ||
 |-
-|[[M(16,9,3)]] || <math>B_0(k \tilde{S}_4)</math><ref>This is the double cover SmallGroup(48,28)</ref> || ? ||8 ||2 ||<math>1</math> || || || ||1 || <math>Q(2 {\cal B})_1</math>
+|[[M(16,11,3)]] || <math>k(S_4 \times C_2)</math> || ? ||10 ||2 ||<math>1</math> || || || ||1 ||
 |-
-|[[M(16,9,4)]] || <math>B_0(kSL_2(9))</math> || 1 ||9 ||3 ||<math>1</math> || || || ||1 || <math>Q(3 {\cal A})_2</math>
+|[[M(16,11,4)]] || <math>B_0(k(PSL_2(9) \times C_2))</math> || ? ||10 ||3 ||<math>1</math> || || || ||1 ||
 |-
-|[[M(16,9,5)]] || <math>B_0(k(2.A_7))</math> || 1 ||10 ||3 ||<math>1</math> || || || ||1 || <math>Q(3 {\cal B})</math>
+|[[M(16,11,5)]] || <math>B_0(k(A_7 \times C_2))</math> || ? ||10 ||3 ||<math>1</math> || || || ||1 ||
 |-
-|[[M(16,9,6)]] || <math>B_0(kSL_2(7))</math> || 1 ||9 ||3 ||<math>1</math> || || || ||1 || <math>Q(3 {\cal K})</math>
+|[[M(16,11,6)]] || <math>B_0(k(PSL_2(7) \times C_2))</math> || ? ||10 ||3 ||<math>1</math> || || || ||1 ||
 |}
-[[M(16,9,2)]] and [[M(16,9,3)]] are derived equivalent over <math>k</math> by [[References|[Ho97]]], in which it is further proved that ''all'' blocks with defect group <math>Q_{16}</math> and two simple modules are derived equivalent (irrespective of the unknown cases in the classification).
 == Notes ==
 <references />

D8xC2 - Revision history

Charles Eaton at 11:21, 4 January 2019

Charles Eaton: Created page with "__NOTITLE__ == Blocks with defect group D_8 \times C_2 == The invariants k(B), k_i(B) and l(B) are determined in Refere..."

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $D_8 \times C_2$ == The invariants $k(B)$ , $k_i(B)$ and $l(B)$ are determined in Refere..."