scholarly journals ON REGULAR GROUPS AND FIELDS

2014 ◽  
Vol 79 (3) ◽  
pp. 826-844 ◽  
Author(s):  
TOMASZ GOGACZ ◽  
KRZYSZTOF KRUPIŃSKI
Keyword(s):  
Conjugacy Class ◽  
Classical Group ◽  
Multiplicative Group ◽  
Finite Extension ◽  
Generic Type ◽  
Common Generalization ◽  
Counter Example ◽  
Minimal Groups ◽  
Unbounded Orbit

AbstractRegular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that each regular field is algebraically closed. Standard arguments show that a generically stable regular field is algebraically closed. LetKbe a regular field which is not generically stable and letpbe its global generic type. We observe that ifKhas a finite extensionLof degreen, thenP(n)has unbounded orbit under the action of the multiplicative group ofL.Known to be true in the minimal context, it remains wide open whether regular, or even quasi-minimal, groups are abelian. We show that if it is not the case, then there is a counter-example with a unique nontrivial conjugacy class, and we notice that a classical group with one nontrivial conjugacy class is not quasi-minimal, because the centralizers of all elements are uncountable. Then, we construct a group of cardinality ω1with only one nontrivial conjugacy class and such that the centralizers of all nontrivial elements are countable.

scholarly journals FINITE CONJUGACY IN ALGEBRAS AND ORDERS

2001 ◽  
Vol 44 (1) ◽  
pp. 201-213 ◽  
Author(s):  
M. A. Dokuchaev ◽  
S. O. Juriaans ◽  
C. Polcino Milies ◽  
M. L. Sobral Singer
Keyword(s):  
Conjugacy Class ◽  
Division Ring ◽  
Multiplicative Group ◽  
Central Element ◽  
Subject Classification ◽  
Group Rings ◽  
2000 Mathematics Subject Classification ◽  
Primary 16U60 ◽  
Finite Conjugacy

AbstractHerstein showed that the conjugacy class of a non-central element in the multiplicative group of a division ring is infinite. We prove similar results for units in algebras and orders and give applications to group rings.AMS 2000 Mathematics subject classification: Primary 16U60. Secondary 16H05; 16S34; 20F24; 20C05

scholarly journals Unit theorems on algebraic tori

1988 ◽  
Vol 112 ◽  
pp. 117-124 ◽  
Author(s):  
Hyun Kwang Kim
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Multiplicative Group ◽  
Finite Extension ◽  
Algebraic Number Field ◽  
Algebraic Tori ◽  
Algebraic Torus

Let k be a p-adic field (a finite extension of Qp) or an algebraic number field (a finite extension of Q). Let T be an algebraic torus defined over k. We denote by the character module of T (i.e. = Hom (T, Gm), where Gm is the multiplicative group.

scholarly journals Hereditarily minimal topological groups

2019 ◽  
Vol 31 (3) ◽  
pp. 619-646 ◽  
Author(s):  
Wenfei Xi ◽  
Dikran Dikranjan ◽  
Menachem Shlossberg ◽  
Daniele Toller
Keyword(s):  
Abelian Groups ◽  
Multiplicative Group ◽  
The Other ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Topological Groups ◽  
Locally Compact ◽  
Abelian Case ◽  
Compact Abelian Groups ◽  
Minimal Groups

Abstract We study locally compact groups having all subgroups minimal. We call such groups hereditarily minimal. In 1972 Prodanov proved that the infinite hereditarily minimal compact abelian groups are precisely the groups {\mathbb{Z}_{p}} of p-adic integers. We extend Prodanov’s theorem to the non-abelian case at several levels. For infinite hypercentral (in particular, nilpotent) locally compact groups, we show that the hereditarily minimal ones remain the same as in the abelian case. On the other hand, we classify completely the locally compact solvable hereditarily minimal groups, showing that, in particular, they are always compact and metabelian. The proofs involve the (hereditarily) locally minimal groups, introduced similarly. In particular, we prove a conjecture by He, Xiao and the first two authors, showing that the group {\mathbb{Q}_{p}\rtimes\mathbb{Q}_{p}^{*}} is hereditarily locally minimal, where {\mathbb{Q}_{p}^{*}} is the multiplicative group of non-zero p-adic numbers acting on the first component by multiplication. Furthermore, it turns out that the locally compact solvable hereditarily minimal groups are closely related to this group.

Tire Treadwear — A Comprehensive Evaluation of the Factors: Generic Type, Aspect Ratio, Tread Pattern, and Tread Composition Part III: Results of Supplementary and UTQG Treadwear Test Series

1986 ◽  
Vol 14 (4) ◽  
pp. 235-263
Author(s):  
A. G. Veith
Keyword(s):  
Carbon Black ◽  
Comprehensive Evaluation ◽  
Work Intensity ◽  
Generic Type ◽  
Aspect Ratios ◽  
Index Variation ◽  
Primary Determinant ◽  
Severity Levels ◽  
High Test ◽  
Better Than

Abstract The effect of tread compound variation on tire treadwear was studied using bias and radial tires of two aspect ratios. Compound variations included types of rubber and carbon black as well as the levels of carbon black, process oil, and curatives. At low to moderate test severity, SBR and an SBR/BR blend performed better than NR while at high test severity NR and SBR were better than the SBR/BR blend. The SBR/BR blend was the best at low severity testing. Higher structure and higher surface area carbon black gave improved treadwear at all severity levels. The concept of a “frictional work intensity” as the primary determinant of treadwear index variation with test severity is proposed. Some factors which influence frictional work intensity are discussed.

Continuity of homotopies

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Open Subset ◽  
Small Neighborhood ◽  
Unit Vector ◽  
Zariski Topology ◽  
Simple Point ◽  
Smooth Variety ◽  
Additional Material ◽  
Generic Type ◽  
Zariski Open Subset

This chapter includes some additional material on homotopies. In particular, for a smooth variety V, there exists an “inflation” homotopy, taking a simple point to the generic type of a small neighborhood of that point. This homotopy has an image that is properly a subset of unit vector V, and cannot be understood directly in terms of definable subsets of V. The image of this homotopy retraction has the merit of being contained in unit vector U for any dense Zariski open subset U of V. The chapter also proves the continuity of functions and homotopies using continuity criteria and constructs inflation homotopies before proving GAGA type results for connectedness. Additional results regarding the Zariski topology are given.

Prolonging Nerve Grafts Using Chemical Extracted Muscle-in-vein with Vein Window Method Chemical acellular nerve grafts

2018 ◽  
Vol 68 (12) ◽  
pp. 2936-2940
Author(s):  
Irina Mihaela Jemnoschi Hreniuc ◽  
Camelia Tamas ◽  
Sorin Aurelian Pasca ◽  
Bogdan Ciuntu ◽  
Roxana Ciuntu ◽  
...  
Keyword(s):  
Classical Group ◽  
Donor Site ◽  
Good Alternative ◽  
Nerve Graft ◽  
Male Rats ◽  
Chemical Extraction ◽  
Nerve Grafting ◽  
Nerve Grafts ◽  
Local Resources ◽  
Window Method

Nerve injuries are a common pathology in hand trauma. The consequences are drastic both for patients and doctors/medical system. In many cases direct coaptation is impossible. A nerve graft should be used in the case of a neuroma, trauma or tumor, for restoration of nervous influx. The aim of this study is demonstrate that by grafting restant nerve stumps with muscle-in-vein nerve grafts we obtain good result in terms of functional and sensibility recovery and also our method �window-vein� is a good way of prolonging nerve grafts. The method of study is experimental. We worked in the laboratory in optimal conditions for carrying out of muscles-in-vein nerve grafts (nerve grafts size 1.5 cm-3 cm). We used acellular muscle grafts with the chemical extraction method.The study was conducted on experimental animals (Wistar male rats).We used 30 experience animals in 3 equal groups (classical group and muscle-in-vein nerve grafts-2 nerve grafts of 1,5 cm central sutured and the third group with muscle-in-vein nerve grafts, window-vein method, 3 cm). At 4 and respectively 6 weeks postoperative at the quality tests we observed the progress with the footprint test. The operated hind in comparison with the healthy hind was 86% recovered and similar with classic nerve grafts. Quantitatively the number of regenerated axons in the group with muscle-in-vein nerve grafts was significant bigger in comparison with the classical group (15%).The method using muscle-in-vein nerve graft with windows-vein it�s a good alternative for nerve grafting in comparison with classical nerve grafting. When the local possibilities are limited, this method is good for prolonging the grafts. The relationship between cost and benefit in this case it�s an advantage because we use the local resources of the affected area. The motor results of nerve grafting ingroup 2 in comparison with group 3 were similar and in some cases better in group 1. Grafting with MVNG offers a better alternative for donor site regeneration in comparison with classical nerve grafts. This method is useful to prolong nerve grafts without adding morbidity.

scholarly journals DIOPHANTINE SETS OF POLYNOMIALS OVER ALGEBRAIC EXTENSIONS OF THE RATIONALS

2014 ◽  
Vol 79 (3) ◽  
pp. 733-747
Author(s):  
CLAUDIA DEGROOTE ◽  
JEROEN DEMEYER
Keyword(s):  
Minimal Polynomial ◽  
Finite Extension ◽  
Algebraic Extension ◽  
Recursively Enumerable

AbstractLet L be a recursive algebraic extension of ℚ. Assume that, given α ∈ L, we can compute the roots in L of its minimal polynomial over ℚ and we can determine which roots are Aut(L)-conjugate to α. We prove that there exists a pair of polynomials that characterizes the Aut(L)-conjugates of α, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in ℝ, or in a finite extension of ℚp (with p an odd prime). Then we show that subsets of L[X]k that are recursively enumerable for every recursive presentation of L[X], are diophantine over L[X].

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