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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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