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 may be applied to the cell complexes for which the function TorsionSubcomplex( groupName, p) has produced no warning. It prints on the screen which cells to merge and which edges to cut off in order to reduce the p-torsion subcomplex without changing the equivariant Farrell cohomology. Finally, it prints the representative cells, their stabilizers and the Abelianization of the latter. |
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