The torsion subcomplexes subpackage has been conceived and implemented by Alexander D. Rahm. |
IsPnormal( G, p)
Inputs a finite group G and a prime p. Checks if the group G is p-normal for the prime p. Zassenhaus defines a finite group to be p-normal if the center of one of its Sylow p-groups is the center of every Sylow p-group in which it is contained. |
TorsionSubcomplex( groupName, p)
Inputs a cell complex with action of a group. In HAP, presently the following cell complexes with stabilisers fixing their cells pointwise are available, specified by the following "groupName" strings: |
DisplayAvailableCellComplexes();
Displays the cell complexes that are available in HAP. |
VisualizeTorsionSkeleton( groupName, p)
Executes the function TorsionSubcomplex( groupName, p) and visualizes its output, namely the incidence matrix of the 1-skeleton of the p-torsion subcomplex, as a graph. |
ReduceTorsionSubcomplex( groupName, p)
This function start with the same operations as the function TorsionSubcomplex( groupName, p), and if the cell stabilisers are fixing their cells pointwise, it continues as follows. |
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