منابع مشابه
On Hurwitz groups of low rank
Let , 3, 7) denote the infinite triangle group, defined by the presentation X,Y | X = Y 3 = (XY ) = 1 . A non-trivial group G is said to be (2, 3, 7) -generated (or a Hurwitz group, when finite) if it is an epimorphic image of , 3, 7). Hurwitz groups are particularly interesting for the theory of Riemann surfaces. Namely, if H is the automorphism group of a compact Riemann surface of genus g > ...
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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...
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let us consider the set of non-abelian finite simple groups which admit non-trivial irreducible projective representations of degree $le 7$ over an algebraically closed field $mathbb{f}$ of characteristic $pgeq 0$. we survey some recent results which lead to the complete list of the groups in this set which are $(2,3,7)$-generated and of those which are $(2,3)$-generated.
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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...
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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...
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2004
ISSN: 1461-1570
DOI: 10.1112/s1461157000001145