Difference between revisions of "Classification by p-group"

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(SmallGroup(16,3) to MNA(2,1))
(Added up to SmallGroup(32,27))
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|32 || [[C4xC4xC2|21]] || [[C4xC4xC2|<math>C_4 \times C_4 \times C_2</math>]] || 2(2) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[EKKS14]]]  
 
|32 || [[C4xC4xC2|21]] || [[C4xC4xC2|<math>C_4 \times C_4 \times C_2</math>]] || 2(2) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[EKKS14]]]  
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|-
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|32 || [[MNA(2,1)xC2|22]] || [[MNA(2,1)xC2|<math>MNA(2,1) \times C_2</math>]] || || || || Invariants known by [[References|[Sa14,10.25]]] ||
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|32 || [[(C4:C4)xC2|23]] || [[(C4:C4)xC2|<math>(C_4:C_4) \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 || [[SmallGroup(32,24)|24]] || [[SmallGroup(32,24)]]<!--<math>(C_4 \times C_4):C_2=\langle a,b,c \mid a^4 = b^4 = c^2 = e, ab = ba, ac = ca, cb = a^2bc \rangle</math>]]--> || 1(1)) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || [[References|[Sa14]]] ||
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|32 || [[D8xC4|25]] || [[D8xC4|<math>D_8 \times C_4</math>]] || || || || Invariants known by [[References|[Sa14,9.7]]] ||
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|32 || [[Q8xC4|26]] || [[Q8xC4|<math>Q_8 \times C_4</math>]] || || || || Invariants known by [[References|[Sa14,9.28]]] ||
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|32 || [[SmallGroup(32,27)|27]] || [[SmallGroup(32,27)]]<!--|<math>(C_4 \times C_4):C_2=\langle x,y,z,a,b \mid x^2 = y^2 = z^2 = a^2 = b^2 = e, xy = yx, xz, = zx, yz = zy, aza^{-1} = xz, bzb^{-1} = yz, ax = xa, ay = ya, bx = xb, by = yb \rangle</math>]]--> || || || || ||
 
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Revision as of 21:39, 17 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 book [Sa14].

Under-construction.png

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

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

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