Projective Special Linear Group of degree 2

URI: https://gptkb.org/entity/Projective_Special_Linear_Group_of_degree_2
GPTKB entity
Statements (33)
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 finite field
gptkbp:firstAppearance 19th century
gptkbp:hasSubgroup dihedral group
Borel subgroup
cyclic group
https://www.w3.org/2000/01/rdf-schema#label Projective Special Linear Group of degree 2
gptkbp:importantFor gptkb:algebraic_geometry
gptkb:geometry
gptkb:Galois_theory
group theory
gptkbp:isA gptkb:group_of_people
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