Difference between revisions of "ApCoCoA-1:GroupsToCheck"
From ApCoCoAWiki
| Line 24: | Line 24: | ||
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.
