Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical group
|
| gptkbp:application |
Automorphism groups of Riemann surfaces
Monodromy groups Symmetry groups of tilings |
| gptkbp:category |
Discrete group
Reflection group Symmetry group Finitely presented group |
| gptkbp:definedIn |
Three generators and three relations
|
| gptkbp:example |
gptkb:(2,3,5)_triangle_group
gptkb:(2,3,7)_triangle_group (2,3,3) triangle group (3,3,3) triangle group |
| gptkbp:field |
gptkb:geometry
gptkb:Group_theory |
| gptkbp:hasSpecialCase |
Finite triangle group
Infinite triangle group |
| https://www.w3.org/2000/01/rdf-schema#label |
Triangle group
|
| gptkbp:introduced |
gptkb:Felix_Klein
|
| gptkbp:loveInterest |
(xyz)^2 = x^p = y^q = z^r = 1
|
| gptkbp:notation |
T(p, q, r)
Δ(p, q, r) |
| gptkbp:order |
Finite if 1/p + 1/q + 1/r > 1
Infinite if 1/p + 1/q + 1/r ≤ 1 |
| gptkbp:relatedTo |
gptkb:Spherical_geometry
gptkb:Weyl_group gptkb:Modular_group gptkb:Euclidean_geometry gptkb:Hyperbolic_geometry modular group |
| gptkbp:bfsParent |
gptkb:Modular_group
|
| gptkbp:bfsLayer |
6
|