Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
discrete group |
| gptkbp:acts_by |
fractional linear transformations
|
| gptkbp:actsOn |
upper half-plane
|
| gptkbp:application |
complex analysis
modular forms number theory elliptic curves |
| gptkbp:centralTo |
{±I}
|
| gptkbp:defines |
group of 2x2 integer matrices with determinant 1
|
| gptkbp:generation |
S = [[0, -1], [1, 0]]
T = [[1, 1], [0, 1]] |
| gptkbp:hasProperty |
non-abelian
orthogonal group finitely generated |
| gptkbp:hasSubgroup |
GL(2, Z)
|
| https://www.w3.org/2000/01/rdf-schema#label |
modular group SL(2, Z)
|
| gptkbp:isomorphicTo |
free product of cyclic groups C_4 and C_6 modulo C_2
|
| gptkbp:isQuotientOf |
gptkb:PSL(2,_Z)
|
| gptkbp:loveInterest |
(ST)^3 = I
S^4 = I |
| gptkbp:notation |
gptkb:SL(2,_Z)
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
infinite
|
| gptkbp:presentedBy |
<S, T | S^4 = I, (ST)^3 = I>
|
| gptkbp:relatedTo |
modular group
modular function modular group congruence subgroups |
| gptkbp:type |
modular group
|
| gptkbp:bfsParent |
gptkb:modular_j-invariant
|
| gptkbp:bfsLayer |
6
|