C25 - Revision history

Charles Eaton at 10:31, 22 November 2018

2018-11-22T10:31:00Z

Charles Eaton at 10:28, 22 November 2018

2018-11-22T10:28:43Z

Charles Eaton: Switched M(25,1,5) and M(25,1,6) to match C5 labellings

2018-09-28T07:14:17Z

Switched M(25,1,5) and M(25,1,6) to match C5 labellings

Charles Eaton: NOTITLE

2018-09-09T12:51:56Z

__NOTITLE__

Charles Eaton at 07:34, 31 August 2018

2018-08-31T07:34:15Z

Charles Eaton: Created page with "== Blocks with defect group $C_{25}$ == These are blocks with cyclic defect groups and so they are described by Brauer trees. There are 12 possible Brauer..."

2018-08-28T10:32:55Z

Created page with "== Blocks with defect group <math>C_{25}</math> == These are blocks with cyclic defect groups and so they are described by Brauer trees. There are 12 possible Brauer..."

New page

== Blocks with defect group <math>C_{25}</math> ==

These are blocks with [[cyclic defect groups]] and so they are described by [[Brauer trees]].

There are 12 possible Brauer trees. It is not known which give rise to <math>\mathcal{O}</math>-Morita equivalence classes.

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

{| 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

|-
|<math>M(25,1,1)</math> || <math>kC_{25}</math> ||25 ||1 || <math>1</math> ||<math>C_{25} : C_{20}</math> || ||1 ||1 ||
|-
|<math>M(25,1,2)</math> || <math>kD_{50}</math> ||14 ||2 || <math>C_2</math> || || ||1 ||1 ||
|-
|<math>M(25,1,3)</math> || <math>B_0(kPSL_2(49))</math> ||14 ||2 || <math>C_2</math> || || ||1 ||1 ||
|-
|<math>M(25,1,4)</math> || <math>k(C_{25}:C_4)</math> ||10 ||4 || <math>C_4</math> || <math>C_4</math> || ||1 ||1 ||
|-
|<math>M(25,1,5)</math> || <math>B_0(kSz(32))</math> ||10 ||4 || <math>C_4</math> || || ||1 ||1 ||
|}

Blocks in <math>M(25,1,2)</math> are derived equivalent (over <math>\mathcal{O}</math>) to those in <math>M(25,1,3)</math>.

Blocks in <math>M(25,1,4)</math> are derived equivalent (over <math>\mathcal{O}</math>) to those in <math>M(25,1,5)</math>.

@@ Line 31: / Line 31: @@
 |[[M(25,1,4)]] || <math>k(C_{25}:C_4)</math> ||10 ||4 || <math>C_4</math> || <math>C_4 \times C_5</math> || ||1 ||1 ||
 |-
-|[[M(25,1,5)]] || <math>B_0(kPGL_2(49))</math> ||10 ||4 || <math>C_4</math> || <math>C_5</math> || ||1 ||1 ||
+|[[M(25,1,5)]] || <math>B_0(kPGL_2(49))</math> ||10 ||4 || <math>C_4</math> || <math>C_2 \times C_5</math> || ||1 ||1 ||
 |-
 |[[M(25,1,6)]] || <math>B_0(kSz(32))</math> ||10 ||4 || <math>C_4</math> || <math>C_5</math> || ||1 ||1 ||

@@ Line 25: / Line 25: @@
 |[[M(25,1,1)]] || <math>kC_{25}</math> ||25 ||1 || <math>1</math> ||<math>C_{25} : C_{20}</math> || ||1 ||1 ||
 |-
-|[[M(25,1,2)]] || <math>kD_{50}</math> ||14 ||2 || <math>C_2</math> || || ||1 ||1 ||
+|[[M(25,1,2)]] || <math>kD_{50}</math> ||14 ||2 || <math>C_2</math> || <math>C_2 \times C_{10}</math> || ||1 ||1 ||
 |-
-|[[M(25,1,3)]] || <math>B_0(kPSL_2(49))</math> ||14 ||2 || <math>C_2</math> || || ||1 ||1 ||
+|[[M(25,1,3)]] || <math>B_0(kPSL_2(49))</math> ||14 ||2 || <math>C_2</math> || <math>C_{10}</math> || ||1 ||1 ||
 |-
-|[[M(25,1,4)]] || <math>k(C_{25}:C_4)</math> ||10 ||4 || <math>C_4</math> || <math>C_4</math> || ||1 ||1 ||
+|[[M(25,1,4)]] || <math>k(C_{25}:C_4)</math> ||10 ||4 || <math>C_4</math> || <math>C_4 \times C_5</math> || ||1 ||1 ||
 |-
-|[[M(25,1,5)]] || <math>B_0(kSz(32))</math> ||10 ||4 || <math>C_4</math> || || ||1 ||1 ||
+|[[M(25,1,5)]] || <math>B_0(kPGL_2(49))</math> ||10 ||4 || <math>C_4</math> || <math>C_5</math> || ||1 ||1 ||
 |-
-|[[M(25,1,6)]] || <math>B_0(kPGL_2(49))</math> ||10 ||4 || <math>C_4</math> || || ||1 ||1 ||
+|[[M(25,1,6)]] || <math>B_0(kSz(32))</math> ||10 ||4 || <math>C_4</math> || <math>C_5</math> || ||1 ||1 ||
 |}

← Older revision		Revision as of 12:51, 9 September 2018
Line 1:		Line 1:
		+	__NOTITLE__
		+
	== Blocks with defect group <math>C_{25}</math> ==		== Blocks with defect group <math>C_{25}</math> ==

@@ Line 21: / Line 21: @@
 |-
-|<math>M(25,1,1)</math> || <math>kC_{25}</math> ||25 ||1 || <math>1</math> ||<math>C_{25} : C_{20}</math> || ||1 ||1 ||
+|[[M(25,1,1)]] || <math>kC_{25}</math> ||25 ||1 || <math>1</math> ||<math>C_{25} : C_{20}</math> || ||1 ||1 ||
 |-
-|<math>M(25,1,2)</math> || <math>kD_{50}</math> ||14 ||2 || <math>C_2</math> || || ||1 ||1 ||
+|[[M(25,1,2)]] || <math>kD_{50}</math> ||14 ||2 || <math>C_2</math> || || ||1 ||1 ||
 |-
-|<math>M(25,1,3)</math> || <math>B_0(kPSL_2(49))</math> ||14 ||2 || <math>C_2</math> || || ||1 ||1 ||
+|[[M(25,1,3)]] || <math>B_0(kPSL_2(49))</math> ||14 ||2 || <math>C_2</math> || || ||1 ||1 ||
 |-
-|<math>M(25,1,4)</math> || <math>k(C_{25}:C_4)</math> ||10 ||4 || <math>C_4</math> || <math>C_4</math> || ||1 ||1 ||
+|[[M(25,1,4)]] || <math>k(C_{25}:C_4)</math> ||10 ||4 || <math>C_4</math> || <math>C_4</math> || ||1 ||1 ||
 |-
-|<math>M(25,1,5)</math> || <math>B_0(kSz(32))</math> ||10 ||4 || <math>C_4</math> || || ||1 ||1 ||
+|[[M(25,1,5)]] || <math>B_0(kSz(32))</math> ||10 ||4 || <math>C_4</math> || || ||1 ||1 ||
 |}

@@ Line 3: / Line 3: @@
 == Blocks with defect group <math>C_{25}</math> ==
-These are blocks with [[cyclic defect groups]] and so they are described by [[Brauer trees]].
+These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
 There are 12 possible Brauer trees. It is not known which give rise to <math>\mathcal{O}</math>-Morita equivalence classes.