Difference between revisions of "Classification by p-group"

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(Blocks for p=2)
(Rest of 32)
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|32 || [[C4:Q8|35]] || [[C4:Q8|<math>C_4:Q_8</math>]] || 1(1) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[Sa14]]] ||
 
|32 || [[C4:Q8|35]] || [[C4:Q8|<math>C_4:Q_8</math>]] || 1(1) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[Sa14]]] ||
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|-
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|32 || [[C8xC2xC2|36]] || [[C8xC2xC2|<math>C_8 \times C_2 \times C_2</math>]] || 3(3) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[EL18a]]] ||
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|-
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|32 || [[M16xC2|37]] || [[M16xC2|<math>M_{16} \times C_2</math>]] || 1(1) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[Sa14]]] ||
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|-
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|32 || [[D8*C8|38]] || [[D8*C8|<math>D_8*C_8</math>]] || || || || Invariants known by [[References|[Sa14,9.18]]] ||
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|-
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|32 || [[D16xC2|39]] || [[D16xC2|<math>D_{16} \times C_2</math>]] || || || || Invariants known by [[References|[Sa14,9.7]]] ||
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|-
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|32 || [[SD16xC2|40]] || [[SD16xC2|<math>SD_{16} \times C_2</math>]] || || || || Invariants known by [[References|[Sa14,9.37]]] ||
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|-
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|32 || [[Q16xC2|41]] || [[Q16xC2|<math>Q_{16} \times C_2</math>]] || || || || Invariants known by [[References|[Sa14,9.28]]] ||
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|-
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|32 || [[D16*C4|42]] || [[D16*C4|<math>D_{16}*C_4</math>]] || || || || Invariants known by [[References|[Sa14,9.18]]] ||
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|-
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|32 || [[SmallGroup(32,43)|43]] || [[SmallGroup(32,43)]] || || || || ||
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|-
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|32 || [[SmallGroup(32,44)|44]] || [[SmallGroup(32,44)]] || || || || ||
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|-
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|32 || [[C4xC2xC2xC2|45]] || [[C4xC2xC2xC2|<math>C_4 \times C_2 \times C_2 \times C_2</math>]] || || || || Invariants known by [[References|[Sa14, 13.9]]] ||
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|-
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|32 || [[D8xC2xC2|46]] || [[D8xC2xC2|<math>D_8 \times C_2 \times C_2</math>]] || || || || ||
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|-
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|32 || [[Q8xC2xC2|47]] || [[Q8xC2xC2|<math>Q_8 \times C_2 \times C_2</math>]] || || || || ||
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|-
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|32 || [[D8*C4xC2|48]] || [[D8*C4xC2|<math>(D_8*C_4) \times C_2</math>]] || || || || ||
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|-
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|32 || [[D8*D8|49]] || [[D8*D8|<math>D8*D8</math>]] || || || || Invariants partly known by [[References|[Sa13c]]] ||
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|-
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|32 || [[D8*Q8|50]] || [[D8*Q8|<math>D8*Q8</math>]] || || || || Invariants partly known by [[References|[Sa13c]]] ||
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|-
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|32 || [[(C2)^5|51]] || [[(C2)^5|<math>(C_2)^5</math>]] || || || || ||
 
|}
 
|}
  

Revision as of 12:43, 31 October 2018

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].

Under-construction.png

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

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

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