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gptkbp:instanceOf
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gptkb:group_of_people
gptkb:discrete_group
|
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gptkbp:acts_by
|
fractional linear transformations
|
|
gptkbp:actsOn
|
upper half-plane
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|
gptkbp:application
|
complex analysis
modular forms
number theory
elliptic curves
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gptkbp:centralTo
|
{±I}
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|
gptkbp:defines
|
group of 2x2 integer matrices with determinant 1
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gptkbp:generation
|
S = [[0, -1], [1, 0]]
T = [[1, 1], [0, 1]]
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gptkbp:hasProperty
|
gptkb:orthogonal_group
non-abelian
finitely generated
|
|
gptkbp:hasSubgroup
|
GL(2, Z)
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gptkbp:isomorphicTo
|
free product of cyclic groups C_4 and C_6 modulo C_2
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gptkbp:isQuotientOf
|
gptkb:PSL(2,_Z)
|
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gptkbp:loveInterest
|
(ST)^3 = I
S^4 = I
|
|
gptkbp:notation
|
gptkb:SL(2,_Z)
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gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
infinite
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gptkbp:presentedBy
|
<S, T | S^4 = I, (ST)^3 = I>
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|
gptkbp:relatedTo
|
gptkb:modular_group
gptkb:modular_function
modular group congruence subgroups
|
|
gptkbp:type
|
gptkb:modular_group
|
|
gptkbp:bfsParent
|
gptkb:SL(2,_R)
|
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gptkbp:bfsLayer
|
7
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
modular group SL(2, Z)
|