# ApCoCoA-1:GroupsToCheck

### Back to Symbolic Data

#### Inserted Groups

Baumslag-Gersten Group

``` Checked: Yes
Notes: --
```

Braid Group

``` Checked: No
Notes:  --
```

Cyclic Group

``` Checked: No
Notes:  --
```

Dicyclic Group

``` Checked: No
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.
```

Dihedral Group

``` Checked: No
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)?
```

von Dyck Group

``` Checked: No
Notes: A useful reference is still missing
```

Free abelian Group

``` Checked: No
Notes: --
```

Free Group

``` Checked: No
Notes: --
```

Fibonacci Group

``` Checked: No
Notes: --
```

Heisenberg Group

``` Checked: No
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: No
Notes: --
```

Ordinary Tetrahedron Groups

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

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.
```