Consider the following group presentation:
Denote by the subgroup of index (http://planetmath.org/Coset) 2 in , corresponding to preservation of of the triangle.
The are defined by the following presentation:
Note that , so is of the .
Arising from the geometrical nature of these groups,
is called the spherical case,
is called the Euclidean case, and
is called the hyperbolic case
Groups either of the form or are referred to as triangle groups; groups of the form are sometimes refered to as von Dyck groups.
|Date of creation||2013-03-22 14:25:07|
|Last modified on||2013-03-22 14:25:07|
|Last modified by||rmilson (146)|
|Defines||von Dyck groups|