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The Torsion Subcomplex subpackage has been conceived and implemented by Bui Anh Tuan and Alexander D. Rahm |

`RigidFacetsSubdivision( X )`
It inputs an n-dimensional G-equivariant CW-complex X on which all the cell stabilizer subgroups in G are finite. It returns an n-dimensional G-equivariant CW-complex Y which is topologically the same as X, but equipped with a G-CW-structure which is rigid. |

` 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( C, p)`
Inputs either a cell complex with action of a group as a variable or a group name. 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( C, p)`
This function start with the same operations as the function TorsionSubcomplex( C, p), and if the cell stabilisers are fixing their cells pointwise, it continues as follows. |

`EquivariantEulerCharacteristic( X )`
It inputs an n-dimensional Γ-equivariant CW-complex X all the cell stabilizer subgroups in Γ are finite. It returns the equivariant euler characteristic obtained by using mass formula ∑_σ(-1)^dimσfrac1card(Γ_σ) |

`CountingCellsOfACellComplex( X )`
It inputs an n-dimensional Γ-equivariant CW-complex X on which all the cell stabilizer subgroups in Γ are finite. It returns the number of cells in X |

`CountingControlledSubdividedCells( X )`
It inputs an n-dimensional Γ-equivariant CW-complex X on which all the cell stabilizer subgroups in Γ are finite. It returns the number of cells in X appear during the subdivision process using the RigidFacetsSubdivision. |

`CountingBaryCentricSubdividedCells( X )`
It inputs an n-dimensional Γ-equivariant CW-complex X on which all the cell stabilizer subgroups in Γ are finite. It returns the number of cells in X appear during the subdivision process using the barycentric subdivision. |

`EquivariantSpectralSequencePage( C, m, n)`
It inputs a triple (C,m,n) where C is either a groupName explained as in TorsionSubcomplex, m is the dimension of the reduced torsion subcomplex, and n is the highest vertical degree in the spectral sequence page. At the moment, the function works only when m=1,i.e, after reduction the torsion subcomplex has degree 1. It returns a component object R consists of the first page of spectral sequence, and i-th cohomology groups for i less than n. |

`ExportHapCellcomplexToDisk( C, groupName)`
It inputs a cell complex C which is stored as a variable in the memory, together with a user's desire name. In case, the input is a torsion cell complex then the user's desire name should be in the form "group_ptorsion" in order to use the function EquivariantSpectralSequencePage. The function will export C to the hard disk. |

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