منابع مشابه
Hurwitz Groups and Surfaces
Hurwitz not only gave an upper bound for the number of automorphisms of a compact Riemann surface of genus greater than 2, but also gave a characterization of which finite groups could be groups of automorphisms achieving this bound. In practice, however, the identification of such groups and of the surfaces they act on is difficult except in special cases. We survey what is known. 1. How I Got...
متن کاملp-adic Hurwitz groups
Herrlich showed that a Mumford curve of genus g > 1 over the p-adic complex field Cp has at most 48(g− 1), 24(g− 1), 30(g− 1) or 12(g− 1) automorphisms as p = 2, 3, 5 or p > 5. The Mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p-adic triangle groups ∆p for p ≤ 5, or in a p-adic quadrangle group p for p > 5. The finite groups attaining these...
متن کاملGraph-theoretic Hurwitz Groups
This paper studies the analogue of Hurwitz groups and surfaces in the context of harmonic group actions on finite graphs. Our main result states that maximal graph groups are exactly the finite quotients of the modular group Γ = 〈 x, y | x2 = y3 = 1 〉 of size at least 6. As an immediate consequence, every Hurwitz group is a maximal graph group, and the final section of the paper establishes a d...
متن کاملVirasoro Groups and Hurwitz Schemes
In this paper we study the Hurwitz scheme in terms of the Sato Grassmannian and the algebro-geometric theory of solitons. We will give a characterization, its equations and a show that there is a group of Virasoro type which uniformizes it.
متن کاملHurwitz Groups: a Brief Survey
Hurwitz groups are the nontrivial finite quotients 2 3 7 of the ( 2 , 3 , 7 ) triangle group (x, y\x — y = (xy) = 1) . This paper gives a brief survey of such groups, their significance, and some of their properties, together with a description of all examples known to the author.
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2007
ISSN: 1461-1570
DOI: 10.1112/s1461157000001303