scholarly journals Complete Classification of Degree 7 for Genus 1

2021 ◽  
pp. 594-603
Author(s):  
Peshawa M. Khudhur
Keyword(s):  
Riemann Surface ◽  
Meromorphic Function ◽  
Symmetric Group ◽  
Compact Riemann Surface ◽  
Complete Classification ◽  
Conjugacy Classes ◽  
Branched Cover ◽  
Transitive Subgroup ◽  
Genus One

Assume that  is a meromorphic fuction of degree n where X is compact Riemann surface of genus g. The meromorphic function gives a branched cover of the compact Riemann surface X. Classes of such covers are in one to one correspondence with conjugacy classes of r-tuples (  of permutations in the symmetric group , in which  and s generate a transitive subgroup G of  This work is a contribution to the classification of all primitive groups of degree 7, where X is of genus one.

Classification of Maximal Fuchsian Subsgroups of Some Bianchi Groups

1991 ◽  
Vol 34 (3) ◽  
pp. 417-422 ◽  
Author(s):  
L. Ya. Vulakh
Keyword(s):  
Quadratic Field ◽  
Complete Classification ◽  
Conjugacy Classes ◽  
Imaginary Quadratic Field ◽  
Ring Of Integers

AbstractLet d = 1,2, or p, prime p ≡ 3 (mod 4). Let Od be the ring of integers of an imaginary quadratic field A complete classification of conjugacy classes of maximal non-elementary Fuchsian subgroups of PSL(2, Od) in PGL(2, Od) is given.

scholarly journals Embedded minimal surfaces of finite topology

2019 ◽  
Vol 2019 (753) ◽  
pp. 159-191 ◽  
Author(s):  
William H. Meeks III ◽  
Joaquín Pérez
Keyword(s):  
Asymptotic Behavior ◽  
Riemann Surface ◽  
Finite Number ◽  
Minimal Surface ◽  
Minimal Surfaces ◽  
Compact Riemann Surface ◽  
Finite Topology ◽  
Compact Boundary ◽  
Interior Points

AbstractIn this paper we prove that a complete, embedded minimal surface M in {\mathbb{R}^{3}} with finite topology and compact boundary (possibly empty) is conformally a compact Riemann surface {\overline{M}} with boundary punctured in a finite number of interior points and that M can be represented in terms of meromorphic data on its conformal completion {\overline{M}}. In particular, we demonstrate that M is a minimal surface of finite type and describe how this property permits a classification of the asymptotic behavior of M.

scholarly journals Topological Classification of Conformal Actions onpq-Hyperelliptic Riemann Surfaces

2007 ◽  
Vol 2007 ◽  
pp. 1-29 ◽  
Author(s):  
Ewa Tyszkowska
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Compact Riemann Surface ◽  
Topological Classification ◽  
Hyperelliptic Riemann Surfaces

A compact Riemann surfaceXof genusg>1is said to bep-hyperellipticifXadmits a conformal involutionρ, for whichX/ρis an orbifold of genusp. If in additionXisq-hyperelliptic, then we say thatXispq-hyperelliptic. Here we study conformal actions onpq-hyperelliptic Riemann surfaces with centralp- andq-hyperelliptic involutions.

Finite Groups with Some Subgroups of Given Order

2013 ◽  
Vol 20 (03) ◽  
pp. 457-462 ◽  
Author(s):  
Jiangtao Shi ◽  
Cui Zhang ◽  
Dengfeng Liang
Keyword(s):  
Finite Groups ◽  
Prime Power ◽  
Solvable Groups ◽  
Complete Classification ◽  
Conjugacy Classes ◽  
Prime Power Order

Let [Formula: see text] be the class of groups of non-prime-power order or the class of groups of prime-power order. In this paper we give a complete classification of finite non-solvable groups with a quite small number of conjugacy classes of [Formula: see text]-subgroups or classes of [Formula: see text]-subgroups of the same order.

scholarly journals Connected Components of the Hurwitz Space for the Symmetric Group of Degree 7

2020 ◽  
Vol 24 (2) ◽  
pp. 129
Author(s):  
Haval M. Mohammed Salih
Keyword(s):  
Symmetric Group ◽  
Monodromy Group ◽  
Riemann Sphere ◽  
Complete Classification ◽  
Connected Components ◽  
Branch Points ◽  
Genus Zero ◽  
Computational Tools ◽  
Hurwitz Space

The Hurwitz space  is the space of genus  covers of the Riemann sphere  with branch points and the monodromy group . Let be the symmetric group . In this paper, we enumerate the connected components of . Our approach uses computational tools, relying on the computer algebra system GAP and the MAPCLASS package, to find the connected components of . This work gives us the complete classification of  primitive genus zero symmetric group of degree seven. 

Groups Whose Proper Subgroups of Infinite Rank Have Polycyclic Conjugacy Classes

2015 ◽  
Vol 22 (02) ◽  
pp. 181-188 ◽  
Author(s):  
Francesco de Giovanni ◽  
Marco Trombetti
Keyword(s):  
Homomorphic Image ◽  
Complete Classification ◽  
Factor Group ◽  
Conjugacy Classes ◽  
Infinite Rank

A group G is called a PC-group if the factor group G/CG(〈x〉G) is polycyclic for each element x of G. It is proved here that if G is a group of infinite rank whose proper subgroups of infinite rank have the property PC, then G itself is a PC-group, provided that G has an abelian non-trivial homomorphic image. Moreover, under the same assumption, a complete classification of minimal non-PC groups is obtained.

scholarly journals Rigidity of maximal holomorphic representations of Kähler groups

2015 ◽  
Vol 26 (14) ◽  
pp. 1550113 ◽  
Author(s):  
Marco Spinaci
Keyword(s):  
Riemann Surface ◽  
Lie Group ◽  
Complete Classification ◽  
Schwarz Lemma ◽  
Connected Components ◽  
Equivariant Map ◽  
Kähler Groups ◽  
Diagonal Embedding

We investigate representations of Kähler groups [Formula: see text] to a semisimple non-compact Hermitian Lie group [Formula: see text] that are deformable to a representation admitting an (anti)-holomorphic equivariant map. Such representations obey a Milnor–Wood inequality similar to those found by Burger–Iozzi and Koziarz–Maubon. Thanks to the study of the case of equality in Royden’s version of the Ahlfors–Schwarz lemma, we can completely describe the case of maximal holomorphic representations. If [Formula: see text], these appear if and only if [Formula: see text] is a ball quotient, and essentially reduce to the diagonal embedding [Formula: see text]. If [Formula: see text] is a Riemann surface, most representations are deformable to a holomorphic one. In that case, we give a complete classification of the maximal holomorphic representations, which thus appear as preferred elements of the respective maximal connected components.

scholarly journals Parabolic generating pairs of genus-one 2-bridge knot groups

2016 ◽  
Vol 25 (05) ◽  
pp. 1650023 ◽  
Author(s):  
Donghi Lee ◽  
Makoto Sakuma
Keyword(s):  
Complete Classification ◽  
Genus One

We show that any parabolic generating pair of a genus-one hyperbolic 2-bridge knot group is equivalent to the upper or lower meridian pair. As an application, we obtain a complete classification of the epimorphisms from 2-bridge knot groups to genus-one hyperbolic 2-bridge knot groups.

scholarly journals THE CLASSIFICATION OF SOME MODULAR FROBENIUS GROUPS

2011 ◽  
Vol 85 (1) ◽  
pp. 11-18 ◽  
Author(s):  
JUANJUAN FAN ◽  
NI DU ◽  
JIWEN ZENG
Keyword(s):  
Normal Subgroup ◽  
Prime Number ◽  
Frobenius Group ◽  
Minimal Normal Subgroup ◽  
Complete Classification ◽  
Conjugacy Classes ◽  
Frobenius Groups

AbstractFix a prime number p. Let G be a p-modular Frobenius group with kernel N which is the minimal normal subgroup of G. We give the complete classification of G when N has three, four or five p-regular conjugacy classes. We also determine the structure of G when N has more than five p-regular conjugacy classes.

scholarly journals Determinant of the Laplacian on Tori of Constant Positive Curvature with one Conical Point

2019 ◽  
Vol 62 (02) ◽  
pp. 341-347 ◽  
Author(s):  
Victor Kalvin ◽  
Alexey Kokotov
Keyword(s):  
Riemann Surface ◽  
Explicit Expression ◽  
Compact Riemann Surface ◽  
Positive Curvature ◽  
Conical Point ◽  
Conical Singularity ◽  
Conformal Metric ◽  
Constant Positive Curvature ◽  
Genus One

AbstractWe find an explicit expression for the zeta-regularized determinant of (the Friedrichs extensions of) the Laplacians on a compact Riemann surface of genus one with conformal metric of curvature $1$ having a single conical singularity of angle $4\unicode[STIX]{x1D70B}$ .

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