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: No
+
   Checked: Done
 
   Notes: A useful reference is still missing
 
   Notes: A useful reference is still missing
 
Free abelian Group
 
Free abelian Group
   Checked: No
+
   Checked: Done
 
   Notes: --
 
   Notes: --
 
Free Group
 
Free Group
   Checked: No
+
   Checked: Done
 
   Notes: --
 
   Notes: --
 
Fibonacci Group
 
Fibonacci Group
   Checked: No
+
   Checked: Done
 
   Notes: --
 
   Notes: --
 
Heisenberg Group
 
Heisenberg Group
   Checked: No
+
   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: No
+
   Checked: Done
 
   Notes: --
 
   Notes: --
 
Ordinary Tetrahedron Groups
 
Ordinary Tetrahedron Groups
 
   Checked: No
 
   Checked: No
   Notes: I used the implicit invers elements: We know that x^{e_1} = 1, it follows that x^{e_1 - 1} is the invers, and so on..   
+
   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.