Classification by p-group

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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.

We use the following notation for Morita equivalence classes of blocks of finite groups with respect to an algebraically closed field k.

[math]M(x,y,z)[/math] is a class consisting of blocks with defect groups of order x, with a representative having defect group SmallGroup(x,y) in GAP/MAGMA labelling. It is the z-th such class.

Note that it is not known that the isomorphism class of a defect group is a Morita invariant, so it could be that [math]M(x,y1,z1)=M(x,y2,z2)[/math] for some [math](y1,z1) \neq (y2,z2)[/math].

Also, at present there is no known example of a k-Morita equivalence class of blocks which splits into more than one Morita equivalence class with respect to a complete discrete valuation ring. If such an example arises, then we will bring in more notation for classes with respect to the d.v.r.

Blocks of defect zero

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

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

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

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