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 p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas

2015 ◽  
Vol 219 ◽  
pp. 269-302
Author(s):  
Kenichi Bannai ◽  
Hidekazu Furusho ◽  
Shinichi Kobayashi
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Theta Function ◽  
Quadratic Field ◽  
Complex Multiplication ◽  
Imaginary Quadratic Field ◽  
Good Reduction ◽  
Ring Of Integers

AbstractConsider an elliptic curve defined over an imaginary quadratic fieldKwith good reduction at the primes abovep≥ 5 and with complex multiplication by the full ring of integersof K. In this paper, we constructp-adic analogues of the Eisenstein-Kronecker series for such an elliptic curve as Coleman functions on the elliptic curve. We then provep-adic analogues of the first and second Kronecker limit formulas by using the distribution relation of the Kronecker theta function.

scholarly journals An explicit Baker-type lower bound of exponential values

2015 ◽  
Vol 145 (6) ◽  
pp. 1153-1182 ◽  
Author(s):  
Anne-Maria Ernvall-Hytönen ◽  
Kalle Leppälä ◽  
Tapani Matala-aho
Keyword(s):  
Lower Bound ◽  
Linear Form ◽  
Quadratic Field ◽  
Rational Numbers ◽  
Rational Points ◽  
Imaginary Quadratic Field ◽  
Ring Of Integers

Let 𝕀 denote an imaginary quadratic field or the field ℚ of rational numbers and let ℤ𝕀denote its ring of integers. We shall prove a new explicit Baker-type lower bound for a ℤ𝕀-linear form in the numbers 1, eα1, . . . , eαm,m⩾ 2, whereα0= 0,α1, . . . ,αmarem+ 1 different numbers from the field 𝕀. Our work gives substantial improvements on the existing explicit versions of Baker’s work about exponential values at rational points. In particular, dependencies onmare improved.

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.

scholarly journals Units in families of totally complex algebraic number fields

2004 ◽  
Vol 2004 (45) ◽  
pp. 2383-2400
Author(s):  
L. Ya. Vulakh
Keyword(s):  
Algebraic Number ◽  
Continued Fraction ◽  
Quadratic Field ◽  
Number Fields ◽  
Imaginary Quadratic Field ◽  
Algebraic Number Fields ◽  
Ring Of Integers ◽  
Multidimensional Continued Fraction ◽  
Fundamental Units

Multidimensional continued fraction algorithms associated withGLn(ℤk), whereℤkis the ring of integers of an imaginary quadratic fieldK, are introduced and applied to find systems of fundamental units in families of totally complex algebraic number fields of degrees four, six, and eight.

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.

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 Algebraic integers as special values of modular units

2011 ◽  
Vol 55 (1) ◽  
pp. 167-179 ◽  
Author(s):  
Ja Kyung Koo ◽  
Dong Hwa Shin ◽  
Dong Sung Yoon
Keyword(s):  
Quadratic Field ◽  
Algebraic Integer ◽  
Imaginary Quadratic Field ◽  
The Other ◽  
Sufficient Condition ◽  
Algebraic Integers ◽  
Dedekind Eta Function ◽  
Ring Of Integers ◽  
Special Values ◽  
Modular Units

AbstractLet $\varphi(\tau)=\eta(\tfrac12(\tau+1))^2/\sqrt{2\pi}\exp\{\tfrac14\pi\ri\}\eta(\tau+1)$, where η(τ) is the Dedekind eta function. We show that if τ0 is an imaginary quadratic argument and m is an odd integer, then $\sqrt{m}\varphi(m\tau_0)/\varphi(\tau_0)$ is an algebraic integer dividing $\sqrt{m}$ This is a generalization of a result of Berndt, Chan and Zhang. On the other hand, when K is an imaginary quadratic field and θK is an element of K with Im(θK) > 0 which generates the ring of integers of K over ℤ, we find a sufficient condition on m which ensures that $\sqrt{m}\varphi(m\theta_K)/\varphi(\theta_K)$ is a unit.

On p-adic height pairings and locally free classgroups of Hopf orders

1998 ◽  
Vol 123 (3) ◽  
pp. 447-459
Author(s):  
A. AGBOOLA
Keyword(s):  
Elliptic Curve ◽  
Quadratic Field ◽  
Homogeneous Spaces ◽  
Complex Multiplication ◽  
Imaginary Quadratic Field ◽  
The Other ◽  
Module Structure ◽  
Galois Module ◽  
Ring Of Integers ◽  
The One

Let E be an elliptic curve with complex multiplication by the ring of integers [Ofr ] of an imaginary quadratic field K. The purpose of this paper is to describe certain connections between the arithmetic of E on the one hand and the Galois module structure of certain arithmetic principal homogeneous spaces arising from E on the other. The present paper should be regarded as a complement to [AT]; we assume that the reader is equipped with a copy of the latter paper and that he is not averse to referring to it from time to time.

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.

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