Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:mathematical_concept |
| gptkbp:actsOn |
gptkb:geometry
|
| gptkbp:centralTo |
trivial for n > 2
Z/2Z for n = 2 |
| gptkbp:definedIn |
PSL(n,Z) = SL(n,Z)/Z(SL(n,Z))
|
| gptkbp:for_n=2 |
PSL(2,Z) acts on upper half-plane
PSL(2,Z) is a Fuchsian group PSL(2,Z) is a non-abelian free product PSL(2,Z) is generated by S and T PSL(2,Z) is not finite PSL(2,Z) is not simple PSL(2,Z) is residually finite PSL(2,Z) is the modular group PSL(2,Z) ≅ C_2 * C_3 PSL(2,Z) ≅ SL(2,Z)/{±I} center of SL(2,Z) is {±I} |
| gptkbp:for_n=3 |
PSL(3,Z) is infinite
|
| gptkbp:for_n>2 |
PSL(n,Z) has property (T) for n ≥ 3
PSL(n,Z) is arithmetic PSL(n,Z) is finitely generated PSL(n,Z) is finitely presented PSL(n,Z) is infinite PSL(n,Z) is linear PSL(n,Z) is not abelian PSL(n,Z) is not amenable PSL(n,Z) is not finite PSL(n,Z) is not free PSL(n,Z) is not nilpotent PSL(n,Z) is not perfect PSL(n,Z) is not simple PSL(n,Z) is not solvable PSL(n,Z) is residually finite center of SL(n,Z) is trivial |
| gptkbp:fullName |
Projective Special Linear Group over the integers
|
| https://www.w3.org/2000/01/rdf-schema#label |
PSL(n,Z)
|
| gptkbp:importantFor |
gptkb:geometry
modular forms number theory algebraic group theory |
| gptkbp:isQuotientOf |
gptkb:SL(n,Z)
center of SL(n,Z) |
| gptkbp:notation |
gptkb:PSL(n,Z)
|
| gptkbp:relatedGroup |
gptkb:group_of_people
modular group orthogonal group discrete group |
| gptkbp:relatedTo |
gptkb:SL(n,Z)
projective linear group |
| gptkbp:bfsParent |
gptkb:SL(n,Z)
|
| gptkbp:bfsLayer |
6
|