Converse Lagrange Theorem Orders and Supersolvable Orders
نویسندگان
چکیده
For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former. We focus on the difference between these two sets of orders, reformulate the work of earlier authors algorithmically, and construct a computer program to enumerate such NSS-CLT orders. We establish several results relating to NSS and CLT orders and, working from our computer-generated data, propose a pair of conjectures and obtain a complete characterization of the most common form of NSS-CLT order.
منابع مشابه
Converse of Lagrange ’ S Theorem ( Clt ) Numbers
A positive integer n is called a CLT number if every group of order n satisfies the converse of Lagrange’s Theorem. In this note, we find all CLT and supersolvable numbers up to 1000. We also formulate some questions about the distribution of these numbers. RÉSUMÉ: Un nombre entier naturel n est appelé nombre CLT si tout groupe d’ordre n satisfait la réciproque du Théorme de Lagrange. Nous déte...
متن کاملThe sorting order on a Coxeter group
Let (W,S) be an arbitrary Coxeter system. For each sequence ω = (ω1, ω2, . . .) ∈ S∗ in the generators we define a partial order—called the ω-sorting order—on the set of group elements Wω ⊆ W that occur as finite subwords of ω. We show that the ω-sorting order is a supersolvable join-distributive lattice and that it is strictly between the weak and strong Bruhat orders on the group. Moreover, t...
متن کاملThe Sinc-Approximating Kernels of Classical Polynomial Interpolation
A classical approach to interpolation of sampled data is polynomial interpolation. However, from the sampling theorem it follows that the ideal approach to interpolation is to convolve the given samples with the sinc function. In this paper we study the properties of the sinc-approximating kernels that can be derived from the Lagrange central interpolation scheme. Both the finite-extent propert...
متن کاملYazd Medical Interns' Knowledge on Legal Rules and Religious Orders in Medicine
Introduction: In addition to precise physical examination and objective observations, it is necessary for students and interns to be knowledgeable about the rules and religious orders in medicine. This study was performed to investigate Yazd interns' knowledge on religious orders and legal rules in medicine. Methods: In this descriptive study performed in educational health centers of Yazd, 12...
متن کاملOrders Modulo A Prime
In this article I develop the notion of the order of an element modulo n, and use it to prove the famous n 2 + 1 lemma as well as a generalization to arbitrary cyclotomic polynomials. References used in preparing this article are included in the last page. §1 Introduction I might as well state one of the main results of this article up front, so the following discussion seems a little more moti...
متن کامل