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triangle groups
A group with this presentation corresponds to a triangle; roughly, the generators are reflections in its sides and its angles are .
Denote by the subgroup of index 2 in , corresponding to preservation of orientation of the triangle.
The are defined by the following presentation:
Note that , so is independent of the order 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.
Defines:
von Dyck groups
Related:
ExamplesOfGroups
Type of Math Object:
Definition
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Reference
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new question: Creating another set with same cardinality. by hkkass
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new Education: Chapter II by rspuzio
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new collection: The Calculus by Davis and Brenke by rspuzio
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new question: Summation Integration Question by trevor.nickle
May 27
new correction: typo+finite measure hypothesis by Filipe


