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7.7.8.0. triangularGroup
Procedure from library fpalgebras.lib (see fpalgebras_lib).
- Usage:
- triangularGroup(g,d); g an integer, d an integer
- Return:
- ring
- Note:
- - the ring contains the ideal I, which contains the required relations
- g gives the number of the example (1 - 14)
- d gives the degreebound for the Letterplace ring
This is a family
The examples are found in
Classification of the finite generalized tetrahedron groups
by Gerhard Rosenberger and Martin Scheer.
The 14 examples are denoted in theorem 2.12
Example:
| LIB "fpalgebras.lib";
def R = triangularGroup(3,10); setring R;
I;
==> I[1]=a(1)*a(2)*a(3)+1
==> I[2]=b(1)*b(2)*b(3)+1
==> I[3]=a(1)*b(2)*a(3)*b(4)*b(5)*a(6)*b(7)*a(8)*b(9)*b(10)+1
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