# Difference between revisions of "ApCoCoA-1:GroupsToCheck"

From ApCoCoAWiki

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suggest that we should try to add as few extra relations as possible. | suggest that we should try to add as few extra relations as possible. | ||

von Dyck Group | von Dyck Group | ||

− | Checked: | + | Checked: Done |

Notes: A useful reference is still missing | Notes: A useful reference is still missing | ||

Free abelian Group | Free abelian Group | ||

− | Checked: | + | Checked: Done |

Notes: -- | Notes: -- | ||

Free Group | Free Group | ||

− | Checked: | + | Checked: Done |

Notes: -- | Notes: -- | ||

Fibonacci Group | Fibonacci Group | ||

− | Checked: | + | Checked: Done |

Notes: -- | Notes: -- | ||

Heisenberg Group | Heisenberg Group | ||

− | Checked: | + | Checked: Done |

Notes: The matrix in the description will be added as a picture, then it will look much better. At the moment we cannot | Notes: The matrix in the description will be added as a picture, then it will look much better. At the moment we cannot | ||

upload pictures to the server, but I contacted Stefan, there will be a solution soon. | upload pictures to the server, but I contacted Stefan, there will be a solution soon. | ||

Higman Group | Higman Group | ||

− | Checked: | + | Checked: Done |

Notes: -- | Notes: -- | ||

Ordinary Tetrahedron Groups | Ordinary Tetrahedron Groups | ||

Checked: No | Checked: No | ||

− | Notes: I used the implicit | + | Notes: I used the implicit inverse elements: We know that x^{e_1} = 1, it follows that x^{e_1 - 1} is the inverse, and so on.. |

Please check, if I'm right. | Please check, if I'm right. | ||

+ | Comment: You are correct. | ||

Lamplighter Group | Lamplighter Group | ||

Checked: No | Checked: No | ||

Notes: Since I cannot implement "for all n in Z" the user has to define a maximum n (= MEMORY.N). Until this boundary | Notes: Since I cannot implement "for all n in Z" the user has to define a maximum n (= MEMORY.N). Until this boundary | ||

the group will be created. | the group will be created. |

## Revision as of 10:56, 23 August 2013

#### Inserted Groups

Baumslag-Gersten Group

Checked: Done Notes: --

Braid Group

Checked: Done Notes: --

Cyclic Group

Checked: Done Notes: --

Dicyclic Group

Checked: Done Notes: I added two different implementations, one with explicit invers elements and one without. I think the second one is the right one. The computation of the first implementation results in a GB with size 2812, the second one with size 901. Comment: The implementation in the page is correct.

Dihedral Group

Checked: Done Notes: It follows, that a^{-1} = a^{2n-1} and that b^{4} = 1 (second equation) --> b^{-1} = b^{3} My question is, do I have to implement the last equation with b^{3} instead of b^{-1} or should I use 4 generators (a invers to c, b invers to d)? Comment: The implementation in the page is already enough for this group. For your question, I would like to suggest that we should try to add as few extra relations as possible.

von Dyck Group

Checked: Done Notes: A useful reference is still missing

Free abelian Group

Checked: Done Notes: --

Free Group

Checked: Done Notes: --

Fibonacci Group

Checked: Done Notes: --

Heisenberg Group

Checked: Done Notes: The matrix in the description will be added as a picture, then it will look much better. At the moment we cannot upload pictures to the server, but I contacted Stefan, there will be a solution soon.

Higman Group

Checked: Done Notes: --

Ordinary Tetrahedron Groups

Checked: No Notes: I used the implicit inverse elements: We know that x^{e_1} = 1, it follows that x^{e_1 - 1} is the inverse, and so on.. Please check, if I'm right. Comment: You are correct.

Lamplighter Group

Checked: No Notes: Since I cannot implement "for all n in Z" the user has to define a maximum n (= MEMORY.N). Until this boundary the group will be created.