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There
is much interest in the ring structure of the mod p cohomology H*(G,Zp)
of p-groups G.
At present these HAP functions work differently to those for integral cohomology in that they rely heavily on matrix algebra and minimal resolutions. More work needs to be done on improving the effeciency of these functions. At present the corresponding Magma functions are very much faster. |
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Let
G be the Sylow 2-subgroup of the Mathieu group M12. This is
a group of order 64 which is SmallGroup(64,135) in the small groups
library. The following HAP commands compute the ring H*(G,Zp)
modulo all elements of degree greater than 10. The ring is returned as
a structure constant algebra A over the field of two elements. |
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gap>
R:=ResolutionPrimePowerGroup(SmallGroup(64,135),10); Resolution of length 10 in characteristic 2 for <pc group of size 64 with 6 generators> . No contracting homotopy available. A partial contracting homotopy is available. gap> A:=ModPCohomologyRing(R); <algebra of dimension 187 over GF(2)> |
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The following additional command shows that the ring H*(G,Zp) is generated by ... and possibly some generators of degree greater than 10. | |||
gap>
S:=ModPRingGenerators(A); |
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