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7.10.2.28 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
- varying g produces a family of examples

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*a*a+1
==> I[2]=b*b*b+1
==> I[3]=a*b*a*b*b*a*b*a*b*b+1