Special Linear Group of 2x2 Integer Matrices

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people orthogonal group
gptkbp:actsOn	upper half-plane
gptkbp:alsoKnownAs	gptkb:SL(2,_Z)
gptkbp:centralTo	{I, -I}
gptkbp:commutatorSubgroup	itself
gptkbp:contains	modular group
gptkbp:containsElement	2x2 matrices with integer entries and determinant 1
gptkbp:definedIn	group of 2x2 integer matrices with determinant 1
gptkbp:generation	S = [[0, -1], [1, 0]] T = [[1, 1], [0, 1]]
gptkbp:hasSubgroup	gptkb:principal_congruence_subgroup gptkb:Hecke_groups congruence subgroups General Linear Group of 2x2 Integer Matrices
gptkbp:hasTorsionElements	true
https://www.w3.org/2000/01/rdf-schema#label	Special Linear Group of 2x2 Integer Matrices
gptkbp:identityElement	matrix inverse 2x2 identity matrix
gptkbp:importantFor	gptkb:geometry modular forms number theory
gptkbp:isAlgebraicGroup	true
gptkbp:isCountable	true
gptkbp:isDiscrete	true
gptkbp:isFinitelyGenerated	true
gptkbp:isHopfian	true
gptkbp:isMatrixGroup	true
gptkbp:isNonAbelian	true
gptkbp:isPerfect	false
gptkbp:isQuotientOf	gptkb:PSL(2,_Z)
gptkbp:isResiduallyFinite	true
gptkbp:isTorsionFree	false
gptkbp:notation	gptkb:SL(2,_Z)
gptkbp:order	infinite
gptkbp:presentedBy	<S, T \| S^4 = I, (ST)^3 = I>
gptkbp:relatedGroup	matrix multiplication
gptkbp:relatedTo	gptkb:hyperbolic_geometry gptkb:Farey_tessellation modular forms automorphic forms modular group continued fractions modular group action
gptkbp:bfsParent	gptkb:SL_2(Z) gptkb:SL_2(ℤ)
gptkbp:bfsLayer	7