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Modular group

In mathematics, the modular group is the projective special linear group PSL ⁡ ( 2 , Z ) {\displaystyle \operatorname {PSL} (2,\mathbb {Z} )} of 2 × 2 {\displaystyle 2\times 2} matrices with integer coefficients and determinant 1 {\displaystyle 1} , such that the matrices A {\displaystyle A} and − A {\displaystyle -A} are identified. The modular group…

History, Congruence subgroups & Relationship to hyperbolic geometry

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Overview

Definition

Number-theoretic properties

Group-theoretic properties

Relationship to hyperbolic geometry

Congruence subgroups

Dyadic monoid

Maps of the torus

Hecke groups

History

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Modular group

Nodes112
Edges111
Triples51
Avg. degree1.98
Density0.017857
Components1

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Modular group

Top relations

related to Congruence subgroups · 8
Modular group → Important, PSL, SL, The, There, This, We, Z/NZ
related to Dyadic monoid · 8
Modular group → Cantor, Koch, Minkowski's, One, Rham, STn1STn2STn3, The, This
related to history · 8
Modular group → Carl Gustav Jakob Jacobi, Erlangen, Felix Klein, However, Joseph Louis Lagrange, Niels Henrik Abel, Richard Dedekind, The
related to Braid group · 5
Modular group → B3, Further, PSL2, SL2, The
related to Hecke groups · 5
Modular group → Erich Hecke, Hecke, Hq, The, The Hecke
related to Relationship to hyperbolic geometry · 5
Modular group → If, In, Möbius, PSL, The
related to Tessellation of the hyperbolic plane · 5
Modular group → Care, PSL, The, There, This
is a · 4
Modular group → dyadic monoid, projective special linear group PSL, so-called moduli space of elliptic curves, subgroup of the group of orientation-preserving isometries of H.Tessellation of the hyperbolic planeThe modular group Γ acts on H
related to Presentation · 2
Modular group → Geometrically, The
related to Definition · 1
Modular group → The

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Important terminology

group modular displaystyle subgroup mathbb psl operatorname subgroups groups plane matrices sl triangle transformations matrix hyperbolic congruence upper half-plane linear

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Modular groupis aprojective special linear group PSL0.90text
Modular groupis asubgroup of the group of orientation-preserving isometries of H.Tessellation of the hyperbolic planeThe modular group Γ acts on H0.90text
Modular groupis aso-called moduli space of elliptic curves0.90text
Modular groupis adyadic monoid0.90text
Modular grouprelated to Braid groupThe0.60section
Modular grouprelated to Braid groupB30.60section
Modular grouprelated to Braid groupSL20.60section
Modular grouprelated to Braid groupPSL20.60section
Modular grouprelated to Braid groupFurther0.60section
Modular grouprelated to Congruence subgroupsImportant0.60section
Modular grouprelated to Congruence subgroupsThere0.60section
Modular grouprelated to Congruence subgroupsSL0.60section

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