In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact...

Hurwitz's theorem (composition algebras) on quadratic forms and nonassociative algebras Hurwitz's automorphisms theorem on Riemann surfaces Hurwitz's...

Hurwitz scheme Hurwitz surface Hurwitz zeta function Hurwitz's automorphisms theorem Hurwitz's theorem (complex analysis) Hurwitz's theorem (composition...

In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional...

quartic is the Hurwitz surface of lowest possible genus; see Hurwitz's automorphisms theorem. Its (orientation-preserving) automorphism group is isomorphic...

number is maximal by virtue of Hurwitz's theorem on automorphisms (Hurwitz 1893). They are also referred to as Hurwitz curves, interpreting them as complex...

duality Branching theorem Hurwitz's automorphisms theorem Identity theorem for Riemann surfaces Riemann–Roch theorem Riemann–Hurwitz formula Farkas & Kra...

Hardy's theorem (complex analysis) Hartogs–Rosenthal theorem (complex analysis) Harnack's theorem (complex analysis) Hurwitz's automorphisms theorem (algebraic...

triangle, and thus, by the proof of Hurwitz's automorphisms theorem, the tiling is the universal tiling that covers all Hurwitz surfaces (the Riemann surfaces...

R ) {\displaystyle \mathrm {PSL} _{2}(\mathbb {R} )} (see Hurwitz's automorphisms theorem). For hyperbolic three-manifolds the lattice of minimal volume...

triangle, and thus, by the proof of Hurwitz's automorphisms theorem, the tiling is the universal tiling that covers all Hurwitz surfaces (the Riemann surfaces...

genus g > 1. The simplest is that the automorphism group of X is finite (see though Hurwitz's automorphisms theorem). More generally, the set of non-constant...

surface divided by g {\displaystyle g} .[citation needed] Under Hurwitz's automorphisms theorem, a smooth connected Riemann surface X {\displaystyle X} of...

automorphism group attains the maximum of 84(g − 1). This bound is due to the Hurwitz automorphisms theorem, which holds for all g > 1. Such "Hurwitz...

{\displaystyle \mathrm {PSL} (2,7).} From Hurwitz's automorphisms theorem, 168 is the maximum possible number of automorphisms of a genus 3 Riemann surface, this...

is the full automorphism group of An: Aut(An) ≅ Sn. Conjugation by even elements are inner automorphisms of An while the outer automorphism of An of order...

proved that all automorphisms of the fundamental group of a surface can be represented by homeomorphisms (the Dehn–Nielsen–Baer theorem). The Dehn–Nielsen...

arithmetic geometers. More precisely, Hurwitz spaces classify isomorphism classes of Galois covers with a given automorphism group G {\displaystyle G} and a...

of real algebras with positive definite forms was delimited by the Hurwitz's theorem (composition algebras). In 1931 Max Zorn introduced a gamma (γ) into...

orientation preserving automorphisms allowed for a genus 4 surface, by Hurwitz's automorphism theorem. Therefore, Bring's surface is not a Hurwitz surface. This...

Generalized Jacobian Moduli of algebraic curves Hurwitz's theorem on automorphisms of a curve Clifford's theorem on special divisors Gonality of an algebraic...

of Riemann surfaces, the first Hurwitz triplet is a triple of distinct Hurwitz surfaces with the identical automorphism group of the lowest possible genus...

one-dimensional group of automorphisms. Hence, the stack M 1 {\displaystyle {\mathcal {M}}_{1}} has dimension 0. It is a non-trivial theorem, proved by Pierre...

group, PΓL, which allows field automorphisms. Cremona group, Cr(Pn(k)) of birational automorphisms; any biregular automorphism is linear, so PGL coincides...

\exists z\mid x-y=z^{2},} and the second formula is stable under field automorphisms. "Real number". Oxford Reference. 2011-08-03. "real". Oxford English...

normed division algebras over R {\displaystyle \mathbb {R} } . By Hurwitz's theorem they are the only ones; the sedenions, the next step in the Cayley–Dickson...

Wilhelm Magnus pointed out in 1974) they were already implicit in Adolf Hurwitz's work on monodromy from 1891. Braid groups may be described by explicit...

groups often have a certain outer automorphism group, but in particular cases, they have other exceptional outer automorphisms. Among families of finite simple...

permit unique factorization, while Hurwitz's does. Quaternions are a concise method of representing the automorphisms of three- and four-dimensional spaces...

O(n) is the group of automorphisms which keep the quadratic polynomials x2 + y2 + ... invariant, F4 is the group of automorphisms of the following set...