Hurwitz group

E904003

finite group mathematical concept

A Hurwitz group is a finite group that attains the maximal possible order of the automorphism group of a compact Riemann surface of given genus, as specified by Hurwitz's bound.

Try in SPARQL Jump to: Statements Referenced by

Statements (46)

Predicate	Object
instanceOf	finite group ⓘ mathematical concept ⓘ
actsOn	Hurwitz surface NERFINISHED ⓘ
appearsIn	classification problems of finite simple groups with given generating triples ⓘ
characterizedBy	attaining maximal possible order of automorphism group of a compact Riemann surface of given genus ⓘ
context	Teichmüller theory and moduli of curves NERFINISHED ⓘ automorphism groups of algebraic curves over the complex numbers ⓘ
definedBy	Hurwitz bound NERFINISHED ⓘ
field	Riemann surface theory ⓘ algebraic geometry ⓘ geometric group theory ⓘ group theory ⓘ
hasExample	PSL(2,13) NERFINISHED ⓘ PSL(2,7) NERFINISHED ⓘ PSL(2,8) NERFINISHED ⓘ PSL(2,q) for infinitely many prime powers q ⓘ alternating group A7 NERFINISHED ⓘ some alternating groups An for suitable n ⓘ some sporadic simple groups ⓘ
hasMaximalityProperty	maximal order of automorphism group among all compact Riemann surfaces of given genus GENERATED ⓘ
hasProperty	acts as full group of conformal automorphisms of some compact Riemann surface ⓘ admits a generating triple of orders 2, 3, and 7 with product 1 ⓘ every Hurwitz group is a quotient of the (2,3,7) triangle group with torsion-free kernel ⓘ infinitely many pairwise non-isomorphic Hurwitz groups exist ⓘ is a quotient of the (2,3,7) triangle group ⓘ is generated by elements of orders 2 and 3 whose product has order 7 ⓘ many Hurwitz groups are non-abelian simple groups ⓘ maximizes symmetry among surfaces of fixed genus ⓘ order is determined by the genus of the associated Hurwitz surface ⓘ realizable as a group of orientation-preserving isometries of a hyperbolic surface ⓘ
lowerBoundOnGenus	2 ⓘ
namedAfter	Adolf Hurwitz NERFINISHED ⓘ
relatedTo	(2,3,7) triangle group NERFINISHED ⓘ Fuchsian group of signature (2,3,7) ⓘ Galois coverings of the Riemann sphere branched over three points ⓘ Hurwitz curve NERFINISHED ⓘ Hurwitz surface NERFINISHED ⓘ automorphism group of a Riemann surface ⓘ compact Riemann surface ⓘ dessins d’enfants NERFINISHED ⓘ finite simple group ⓘ hyperbolic geometry ⓘ triangle group ⓘ
satisfies	\|G\| = 84(g-1) for some compact Riemann surface of genus g ≥ 2 ⓘ
usedIn	construction of highly symmetric Riemann surfaces ⓘ study of extremal automorphism groups of curves ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Hurwitz bound on automorphism groups of curves → relatedConcept → Hurwitz group ⓘ