Projective Special Linear Group of degree 2

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people
gptkbp:abbreviation	gptkb:PSL(2,_q)
gptkbp:actsOn	projective line over finite field
gptkbp:alsoKnownAs	gptkb:PSL2
gptkbp:automorphismGroup	PGL(2, q)
gptkbp:centralTo	order 2 (for even q) trivial (for odd q)
gptkbp:definedIn	gptkb:finite_field
gptkbp:firstAppearance	gptkb:19th_century
gptkbp:hasSubgroup	gptkb:cyclic_group gptkb:dihedral_group Borel subgroup
gptkbp:importantFor	gptkb:algebraic_geometry gptkb:geometry gptkb:Galois_theory group theory
gptkbp:isA	gptkb:group_of_people gptkb:projective_linear_group
gptkbp:isNonAbelian	true (for q > 2)
gptkbp:isomorphicTo	A4 (for PSL(2,3)) A5 (for PSL(2,5)) S3 (for PSL(2,2))
gptkbp:isQuotientOf	gptkb:Special_Linear_Group_of_degree_2 center of SL(2, q)
gptkbp:isSimple	true (for q > 3)
gptkbp:namedFor	mathematicians studying group theory
gptkbp:notation	gptkb:PSL(2,_q)
gptkbp:order	q(q^2-1)/gcd(2, q-1)
gptkbp:usedIn	classification of finite simple groups
gptkbp:bfsParent	gptkb:PSL2 gptkb:Special_Linear_Group_of_degree_2
gptkbp:bfsLayer	7
https://www.w3.org/2000/01/rdf-schema#label	Projective Special Linear Group of degree 2