Maximal Order of an NG-group

2021 ◽  
Author(s):  
Professor Faraj Abunabi
Keyword(s):  
Maximal Order

Maximal Order of an NG-group

2021 ◽  
pp. 33-38
Author(s):  
Faraj. A. Abdunabi
Keyword(s):  
Permutation Group ◽  
Equivalence Relation ◽  
Maximal Order ◽  
Quotient Set

This study was aimed to consider the NG-group that consisting of transformations on a nonempty set A has no bijection as its element. In addition, it tried to find the maximal order of these groups. It found the order of NG-group not greater than n. Our results proved by showing that any kind of NG-group in the theorem be isomorphic to a permutation group on a quotient set of A with respect to an equivalence relation on A. Keywords: NG-group; Permutation group; Equivalence relation; -subgroup

scholarly journals Automorphy factors for a Hilbert modular group

1988 ◽  
Vol 30 (2) ◽  
pp. 231-236
Author(s):  
Shigeaki Tsuyumine
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Rational Number ◽  
Modular Group ◽  
Algebraic Number Field ◽  
Maximal Order ◽  
Hilbert Modular Group ◽  
Hilbert Modular ◽  
Totally Real

Let K be a totally real algebraic number field of degree n > 1, and let OK be the maximal order. We denote by гk, the Hilbert modular group SL2(OK) associated with K. On the extent of the weight of an automorphy factor for гK, some restrictions are imposed, not as in the elliptic modular case. Maass [5] showed that the weight is integral for K = ℚ(√5). It was shown by Christian [1] that for any Hilbert modular group it is a rational number with the bounded denominator depending on the group.

scholarly journals The Maximal Order of Hyper-($b$-ary)-expansions

10.37236/5441 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Michael Coons ◽  
Lukas Spiegelhofer
Keyword(s):  
Recent Result ◽  
Nonnegative Integer ◽  
Maximal Order ◽  
General Integral ◽  
Integral Bases

Using methods developed by Coons and Tyler, we give a new proof of a recent result of Defant, by determining the maximal order of the number of hyper-($b$-ary)-expansions of a nonnegative integer $n$ for general integral bases $b\geqslant 2$.

scholarly journals Core entropy of polynomials with a critical point of maximal order

2019 ◽  
Vol 39 (1) ◽  
pp. 115-130
Author(s):  
Domingo González ◽  
◽  
Gamaliel Blé
Keyword(s):  
Critical Point ◽  
Maximal Order

scholarly journals Unique factorisation rings

1992 ◽  
Vol 35 (2) ◽  
pp. 255-269 ◽  
Author(s):  
A. W. Chatters ◽  
M. P. Gilchrist ◽  
D. Wilson
Keyword(s):  
Prime Ideal ◽  
Prime Ring ◽  
Polynomial Identity ◽  
Noetherian Ring ◽  
Basic Theory ◽  
Maximal Order ◽  
Prime Element ◽  
Polynomial Extension ◽  
Simple Ring ◽  
Left And Right

Let R be a ring. An element p of R is a prime element if pR = Rp is a prime ideal of R. A prime ring R is said to be a Unique Factorisation Ring if every non-zero prime ideal contains a prime element. This paper develops the basic theory of U.F.R.s. We show that every polynomial extension in central indeterminates of a U.F.R. is a U.F.R. We consider in more detail the case when a U.F.R. is either Noetherian or satisfies a polynomial identity. In particular we show that such a ring R is a maximal order, that every height-1 prime ideal of R has a classical localisation in which every two-sided ideal is principal, and that R is the intersection of a left and right Noetherian ring and a simple ring.

Groups with boundedly many commutators of maximal order

2021 ◽  
Vol 567 ◽  
pp. 269-283
Author(s):  
P. Longobardi ◽  
M. Maj ◽  
P. Shumyatsky ◽  
G. Traustason
Keyword(s):  
Maximal Order

scholarly journals A characterization of supersmoothness of multivariate splines

2020 ◽  
Vol 46 (5) ◽  
Author(s):  
Michael S. Floater ◽  
Kaibo Hu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Order ◽  
Maximal Order ◽  
Spline Functions ◽  
Multivariate Splines ◽  
The Finite Element Method ◽  
Polynomial Splines ◽  
Element Method

Abstract We consider spline functions over simplicial meshes in $\mathbb {R}^{n}$ ℝ n . We assume that the spline pieces join together with some finite order of smoothness but the pieces themselves are infinitely smooth. Such splines can have extra orders of smoothness at a vertex, a property known as supersmoothness, which plays a role in the construction of multivariate splines and in the finite element method. In this paper, we characterize supersmoothness in terms of the degeneracy of spaces of polynomial splines over the cell of simplices sharing the vertex, and use it to determine the maximal order of supersmoothness of various cell configurations.

Maximal Order and Order of Information for Numerical Quadrature

1979 ◽  
Vol 26 (3) ◽  
pp. 527-537 ◽  
Author(s):  
Arthur G. Werschulz
Keyword(s):  
Maximal Order ◽  
Numerical Quadrature

scholarly journals Constructing supersingular elliptic curves with a given endomorphism ring

2014 ◽  
Vol 17 (A) ◽  
pp. 71-91 ◽  
Author(s):  
Ilya Chevyrev ◽  
Steven D. Galbraith
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Endomorphism Ring ◽  
Quaternion Algebra ◽  
Maximal Order ◽  
Running Time ◽  
Successive Minima ◽  
Supersingular Elliptic Curves ◽  
Class Polynomials ◽  
Theoretical Results

AbstractLet $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathcal{O}$ be a maximal order in the quaternion algebra $B_p$ over $\mathbb{Q}$ ramified at $p$ and $\infty $. The paper is about the computational problem: construct a supersingular elliptic curve $E$ over $\mathbb{F}_p$ such that ${\rm End}(E) \cong \mathcal{O}$. We present an algorithm that solves this problem by taking gcds of the reductions modulo $p$ of Hilbert class polynomials.New theoretical results are required to determine the complexity of our algorithm. Our main result is that, under certain conditions on a rank three sublattice $\mathcal{O}^T$ of $\mathcal{O}$, the order $\mathcal{O}$ is effectively characterized by the three successive minima and two other short vectors of $\mathcal{O}^T\! .$ The desired conditions turn out to hold whenever the $j$-invariant $j(E)$, of the elliptic curve with ${\rm End}(E) \cong \mathcal{O}$, lies in $\mathbb{F}_p$. We can then prove that our algorithm terminates with running time $O(p^{1+\varepsilon })$ under the aforementioned conditions.As a further application we present an algorithm to simultaneously match all maximal order types with their associated $j$-invariants. Our algorithm has running time $O(p^{2.5 + \varepsilon })$ operations and is more efficient than Cerviño’s algorithm for the same problem.

On the maximal order in PC-codes

Computing ◽  
1978 ◽  
Vol 20 (3) ◽  
pp. 273-278 ◽  
Author(s):  
H. J. Stetter
Keyword(s):  
Maximal Order
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