scholarly journals Generalized torsion elements and hyperbolic links

2020 ◽  
Vol 29 (11) ◽  
pp. 2050079
Author(s):  
Masakazu Teragaito
Keyword(s):  
Identity Element ◽  
Fundamental Groups ◽  
Finite Product ◽  
Torsion Element ◽  
Type Formula ◽  
Group A

In a group, a generalized torsion element is a non-identity element whose some non-empty finite product of its conjugates yields the identity. Such an element is an obstruction for a group to be bi-orderable. We show that the Weeks manifold, the figure-eight sister manifold, and the complement of Whitehead sister link admit generalized torsion elements in their fundamental groups. In particular, the Whitehead sister link, which is the pretzel link of type [Formula: see text], can be generalized to hyperbolic pretzel links of type [Formula: see text]. These give the first examples of hyperbolic links whose link groups admit generalized torsion elements.

scholarly journals On product-one sequences over dihedral groups

2020 ◽  
pp. 2250064
Author(s):  
Alfred Geroldinger ◽  
David J. Grynkiewicz ◽  
Jun Seok Oh ◽  
Qinghai Zhong
Keyword(s):  
Finite Group ◽  
Identity Element ◽  
Finite Sequence ◽  
Finitely Generated ◽  
Dihedral Groups ◽  
Group A ◽  
Arithmetic Combinatorics ◽  
A Finite Group ◽  
Extremal Properties

Let [Formula: see text] be a finite group. A sequence over [Formula: see text] means a finite sequence of terms from [Formula: see text], where repetition is allowed and the order is disregarded. A product-one sequence is a sequence whose elements can be ordered such that their product equals the identity element of the group. The set of all product-one sequences over [Formula: see text] (with the concatenation of sequences as the operation) is a finitely generated C-monoid. Product-one sequences over dihedral groups have a variety of extremal properties. This paper provides a detailed investigation, with methods from arithmetic combinatorics, of the arithmetic of the monoid of product-one sequences over dihedral groups.

scholarly journals Generalized Torsion Elements and Bi-orderability of 3-manifold Groups

2017 ◽  
Vol 60 (4) ◽  
pp. 830-844 ◽  
Author(s):  
Kimihiko Motegi ◽  
Masakazu Teragaito
Keyword(s):  
Fundamental Groups ◽  
Orderable Group ◽  
Torsion Element ◽  
Standard Generator

AbstractIt is known that a bi-orderable group has no generalized torsion element, but the converse does not hold in general. We conjecture that the converse holds for the fundamental groups of 3-manifolds and verify the conjecture for non-hyperbolic, geometric 3-manifolds. We also confirm the conjecture for some infinite families of closed hyperbolic 3-manifolds. In the course of the proof, we prove that each standard generator of the Fibonacci group F(2,m) (m > 2) is a generalized torsion element.

scholarly journals Suatu Kajian Tentang B-Aljabar

2021 ◽  
Vol 3 (2) ◽  
pp. 118
Author(s):  
Wahidah Sanusi ◽  
Muhammad Abdy ◽  
Sahlan Sidjara ◽  
Asriani Arsita Asni
Keyword(s):  
Identity Element ◽  
Finite Sets ◽  
Natural Mapping ◽  
Group A ◽  
Infinite Sets ◽  
Isomorphism Theorems

Abstrak. Penelitian ini merupakan penelitian kajian kepustakaan yang bertujuan untuk mengkaji konsep dan sifat-sifat terkait B-Aljabar. Konsep B-Aljabar dalam penelitian ini berdasarkan penelitian yang telah dilakukan oleh Neggers dan Kim serta Allen. Seluruh pembahasan dalam penelitian ini menggunakan himpunan tegas, baik himpunan berhingga maupun himpunan tidak berhingga. Hasilnya, dapat diberikan bukti yang lebih lengkap dari sifat-sifat B-Aljabar serta hubungannya dengan grup. Suatu grup dengan definisi operasi khusus dan elemen identitas  merupakan B-Aljabar. Lebih lanjut dapat diturunkan beberapa teorema grup kedalam B-Aljabar seperti pemetaan natural dan Teorema Isomorfisma 1 yang dalam pembuktiannya memiliki kemiripan dengan pembuktian pada grup dengan tetap menggunakan sifat-sifat B-Aljabar itu sendiri.Kata Kunci: B-Aljabar, B-Subaljabar, B-Homomorfisma, B-IsomorfismaAbstract. This research is a literature studies that aims at reviewing the concepts and properties of B-Algebras. The concept of B-Algebras in this article is based on research that has been done by Neggers and Kim and Allen. All discussions in this article use the firm sets, both finite sets and infinite sets. As a result, more complete evidence of the properties of B-Algebras can be given and its relationship with the group. A group with a specific operation and has  as an identity element is a B-Algebras. Moreover, a number of group theorems can be derived into B-Algebra such as natural mapping and the First Isomorphism Theorems which in their proof have similarities to the proofs of groups while still using the properties of B-Algebra itself.Keywords: B-Algebras, B-Subalgebras, B-Homomorphism, B-Isomorphism

scholarly journals Generalized Torsion in Knot Groups

2016 ◽  
Vol 59 (01) ◽  
pp. 182-189 ◽  
Author(s):  
Geoff Naylor ◽  
Dale Rolfsen
Keyword(s):  
Fundamental Group ◽  
Torus Knots ◽  
Torsion Element ◽  
Nonidentity Element ◽  
Group A

Abstract In a group, a nonidentity element is called a generalized torsion element if some product of its conjugates equals the identity. We show that for many classical knots one can ûnd generalized torsion in the fundamental group of its complement, commonly called the knot group. It follows that such a group is not bi-orderable. Examples include all torus knots, the (hyperbolic) knot 52, and algebraic knots in the sense of Milnor.

The fundamental groups of Galois covers of planar Zappatic deformations of type Ek

2019 ◽  
Vol 29 (06) ◽  
pp. 905-925
Author(s):  
Meirav Amram ◽  
Cheng Gong ◽  
Sheng-Li Tan ◽  
Mina Teicher ◽  
Wan-Yuan Xu
Keyword(s):  
Fundamental Groups ◽  
Generic Fiber ◽  
Type Formula ◽  
Chern Numbers ◽  
Galois Covers ◽  
Simply Connected

In this paper, we investigate the fundamental groups of Galois covers of planar Zappatic deformations of type [Formula: see text]. Using Moishezon–Teicher’s algorithm, we prove that the Galois covers of the generic fiber of planar Zappatic deformations of type [Formula: see text] [Formula: see text] are simply-connected; we also compute their Chern numbers.

Electron microscopic radioautographic studies on the incorporation of 3H proline in the glomerular basement membrane (GBM) in antistreptococcal-cell-membrane (SCM) injected mice

1984 ◽  
Vol 42 ◽  
pp. 188-189
Author(s):  
R.P. Nayyar ◽  
C.F. Lange ◽  
J. L. Borke
Keyword(s):  
Body Weight ◽  
Cell Membrane ◽  
Basement Membrane ◽  
Glomerular Basement Membrane ◽  
Mesangial Matrix ◽  
Electron Microscopic ◽  
Group A ◽  
Injection Protocol

Streptococcal cell membrane (SCM) antiserum injected mice show a significant thickening of glomerular basement membrane (GBM) and an increase in mesangial matrix within 4 to 24 hours of antiserum administration (1,2,3). This study was undertaken to evaluate the incorporation of 3H proline into glomerular cells and GBM under normal and anti-SCM induced conditions. Mice were administered, intraperitoneally, 0.1 ml of normal or anti-SCM serum followed by a 10 µC/g body weight injection of 3H proline. Details of the preparation of anti-SCM (Group A type 12 streptococcal pyogenes) and other sera and injection protocol have been described elsewhere (2). After 15 minutes of isotope injection a chase of cold proline was given and animal sacrificed at 20 minutes, 1,2,4,8,24 and 48 hours. One of the removed kidneys was processed for immunofluorescence, light and electron microscopic radioautographic studies; second kidney was used for GBM isolation and aminoacid analysis.

An ultrastructural study of sertoli cells in two geographically isolated populations of Aphanius dispar

1992 ◽  
Vol 50 (1) ◽  
pp. 548-549
Author(s):  
Taber A. Ba-Omar ◽  
Philip F. Prentis
Keyword(s):  
Ultrastructural Level ◽  
Uranyl Acetate ◽  
Freshwater Teleost ◽  
Isolated Populations ◽  
En Bloc ◽  
The North ◽  
Group A ◽  
Ultrathin Sections ◽  
Group B ◽  
Geographically Isolated

We have recently carried out a study of spermiogenic differentiation in two geographically isolated populations of Aphanius dispar (freshwater teleost), with a view to ascertaining variation at the ultrastructural level. The sampling areas were the Jebel Al Akhdar in the north (Group A) and the Dhofar region (Group B) in the south. Specimens from each group were collected, the testes removed, fixed in Karnovsky solution, post fixed in OsO, en bloc stained with uranyl acetate and then routinely processed to Agar 100 resin, semi and ultrathin sections were prepared for study.

Cultural and Linguistic Adaptation of the Consensus Auditory-Perceptual Evaluation of Voice (CAPE-V) Into Hindi

2020 ◽  
Vol 63 (12) ◽  
pp. 3974-3981
Author(s):  
Ashwini Joshi ◽  
Isha Baheti ◽  
Vrushali Angadi
Keyword(s):  
Strong Correlation ◽  
Concurrent Validity ◽  
Interrater Reliability ◽  
Voice Quality ◽  
Weak Correlation ◽  
Voice Assessment ◽  
Perceptual Evaluation ◽  
Severity Grade ◽  
Normal Voice ◽  
Group A

Aim The purpose of this study was to develop and assess the reliability of a Hindi version of the Consensus Auditory-Perceptual Evaluation of Voice (CAPE-V). Reliability was assessed by comparing Hindi CAPE-V ratings with English CAPE-V ratings and by the Grade, Roughness, Breathiness, Asthenia and Strain (GRBAS) scale. Method Hindi sentences were created to match the phonemic load of the corresponding English CAPE-V sentences. The Hindi sentences were adapted for linguistic content. The original English and adapted Hindi CAPE-V and GRBAS were completed for 33 bilingual individuals with normal voice quality. Additionally, the Hindi CAPE-V and GRBAS were completed for 13 Hindi speakers with disordered voice quality. The agreement of CAPE-V ratings was assessed between language versions, GRBAS ratings, and two rater pairs (three raters in total). Pearson product–moment correlation was completed for all comparisons. Results A strong correlation ( r > .8, p < .01) was found between the Hindi CAPE-V scores and the English CAPE-V scores for most variables in normal voice participants. A weak correlation was found for the variable of strain ( r < .2, p = .400) in the normative group. A strong correlation ( r > .6, p < .01) was found between the overall severity/grade, roughness, and breathiness scores in the GRBAS scale and the CAPE-V scale in normal and disordered voice samples. Significant interrater reliability ( r > .75) was present in overall severity and breathiness. Conclusions The Hindi version of the CAPE-V demonstrates good interrater reliability and concurrent validity with the English CAPE-V and the GRBAS. The Hindi CAPE-V can be used for the auditory-perceptual voice assessment of Hindi speakers.

A Test of Satiation as a Function of Adaptation in Stuttering

1969 ◽  
Vol 12 (1) ◽  
pp. 110-117 ◽  
Author(s):  
Harold A. Peterson ◽  
Mary Beth Rieck ◽  
Rita K. Hoff
Keyword(s):  
Semantic Differential ◽  
Repeated Readings ◽  
Group A ◽  
Relationship Of ◽  
The Relationship

To test the relationship of adaptation and satiation as hypothesized by Jakobovits, satiation of meaning as a function of repeated readings for adaptation was measured in the performance of 14 male stutterers. The subjects as a group exhibited both satiation and adaptation, but the two phenomena did not occur simultaneously in a significant number of the members of the group. A reduction in meaningfulness, as measured by the semantic differential, was not shown to be a significant factor in the reduction of stuttering frequency for the individuals in the group. Satiation and adaptation were not established as the same phenomenon, although the two may still be related through another factor.

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