Difference between revisions of "Classification by p-group"

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m (Blocks for p=2)
(Blocks for p=2)
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|16 || [[M16|6]] || [[M16|<math>M_{16}</math>]] || <math>\mathcal{O}</math> || 1(1) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[CG12], [Sa12b] ]] ||  
 
|16 || [[M16|6]] || [[M16|<math>M_{16}</math>]] || <math>\mathcal{O}</math> || 1(1) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[CG12], [Sa12b] ]] ||  
 
|-
 
|-
|16 || [[D16|7]] || [[D16|<math>D_{16}</math>]] || <math>k</math>|| 5(?) || <math>k</math> || <math>k</math> || [[References|[Er87]]] ||
+
|16 || [[D16|7]] || [[D16|<math>D_{16}</math>]] || <math>k</math>|| 5(?) || <math>k</math> || <math>k</math> || [[References|[Er87]]] ||  
 
|-
 
|-
 
|16 || [[SD16|8]] || [[SD16|<math>SD_{16}</math>]] || <math>k</math> || 8(?) || || || [[References|[Er88c], [Er90b]]] || Two other possible classes
 
|16 || [[SD16|8]] || [[SD16|<math>SD_{16}</math>]] || <math>k</math> || 8(?) || || || [[References|[Er88c], [Er90b]]] || Two other possible classes
 
|-
 
|-
|16 || [[Q16|9]] || [[Q16|<math>Q_{16}</math>]] || No || 6(?) || || <math>k</math> || [[References|[Er88a], [Er88b], [Ho97]]] || Two possibly infinite families
+
|16 || [[Q16|9]] || [[Q16|<math>Q_{16}</math>]] || No || 6(?) || || <math>k</math> || [[References|[Er88a], [Er88b], [Ho97]]] || Two possibly infinite families when <math>l(B)=2</math>. Classified over <math>\mathcal{O}</math> when <math>l(B)=3</math> in [[References#E|[Ei16]]]
 
|-
 
|-
 
|16 || [[C4xC2xC2|10]] || [[C4xC2xC2|<math>C_4 \times C_2 \times C_2</math>]]|| <math>\mathcal{O}</math> || 3(3) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[EL18a]]] ||
 
|16 || [[C4xC2xC2|10]] || [[C4xC2xC2|<math>C_4 \times C_2 \times C_2</math>]]|| <math>\mathcal{O}</math> || 3(3) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[EL18a]]] ||

Revision as of 16:15, 28 January 2019

Classification of Morita equivalences for blocks with a given defect group

On this page we list classifications of Morita equivalence classes for each isomorphism class of p-groups in turn. Generic classifications for classes of p-groups can be found here.

See this page for a description of the labelling conventions.

Blocks of defect zero

Blocks for [math] p=2 [/math]

The following takes as its starting point Table 13.1 of Sambale's book [Sa14].

Blocks for [math]p=3[/math]

Blocks for [math]p=5[/math]

Blocks for [math]p\geq 7[/math]