scholarly journals A new test for asphericity and diagrammatic reducibility of group presentations

2019 ◽  
Vol 150 (2) ◽  
pp. 871-895 ◽  
Author(s):  
Jonathan Ariel Barmak ◽  
Elias Gabriel Minian
Keyword(s):  
Weak Version ◽  
Zero Divisors ◽  
Group Presentations ◽  
Equations Over Groups ◽  
Weight Test

AbstractWe present a new test for studying asphericity and diagrammatic reducibility of group presentations. Our test can be applied to prove diagrammatic reducibility in cases where the classical weight test fails. We use this criterion to generalize results of J. Howie and S.M. Gersten on asphericity of LOTs and of Adian presentations, and derive new results on solvability of equations over groups. We also use our methods to investigate a conjecture of S.V. Ivanov related to Kaplansky's problem on zero divisors: we strengthen Ivanov's result for locally indicable groups and prove a weak version of the conjecture.

Spherical diagrams and equations over groups

1984 ◽  
Vol 96 (2) ◽  
pp. 255-268 ◽  
Author(s):  
James Howie
Keyword(s):  
Group Presentations ◽  
Equations Over Groups ◽  
Dual Notion ◽  
Original Approach

Spherical diagrams were introduced by Lyndon and Schupp[14] in order to study asphericity in group presentations and in 2-complexes. They have since been studied by several authors [2, 3, 5]. In particular, some technical loopholes in the original approach were closed in [5]. For many purposes the dual notion of pictures, introduced by Rourke[17], is more useful. These arise naturally through transversality. Pictures have also been studied and applied in [2, 5, 6, 12, 19].

Asphericity Tests

1997 ◽  
Vol 07 (04) ◽  
pp. 415-431 ◽  
Author(s):  
Anton A. Klyachko
Keyword(s):  
Free Groups ◽  
Equations Over Groups ◽  
Weight Test ◽  
Special Case ◽  
Torsion Free

In paper [5] the classical Kervaire-Laudenbach conjecture for torsion-free groups is proved. The proof is based on an amazing geometrical fact. Here we prove that this fact is a special case of a statement similar to the well-known Bogley-Pride weight test [2]. This article describes all analogous tests and demonstrates some of their applications to the theory of equations over groups.

scholarly journals A Weak Version of the Strong Exponential Closure

2021 ◽  
Author(s):  
Paola D’Aquino ◽  
Antongiulio Fornasiero ◽  
G. Terzo
Keyword(s):  
Weak Version

scholarly journals 1125. Innovative Virtual Learning in the Midst of a Pandemic - Patients, Populations, and Pandemics: Responding to COVID-19

2020 ◽  
Vol 7 (Supplement_1) ◽  
pp. S592-S593
Author(s):  
Lucille K Kohlenberg ◽  
Muriel J Solberg ◽  
Fatima N Ali-Mirza ◽  
Sheela Shenoi ◽  
Saad Omer
Keyword(s):  
Student Participation ◽  
Lessons Learned ◽  
Direct Patient Care ◽  
Future Health ◽  
Unique Challenge ◽  
Student Groups ◽  
Group Presentations ◽  
Innovative Learning ◽  
Education Medical ◽  
Virtual Setting

Abstract Background The COVID-19 pandemic has posed a unique challenge to undergraduate medical education. Medical schools postponed student participation in direct patient care in mid-March 2020, creating the need for rapidly-designed, virtual, and innovative learning experiences. Methods Utilizing Kern’s six-step approach to curriculum development, faculty and medical student liaisons rapidly designed a six-week online and interactive course for clerkship-year students and above, launched on March 30th, 2020. “Patients, Populations, and Pandemics: Responding to COVID-19” emphasized honing higher level skills of Bloom’s taxonomy, namely evaluating, synthesizing, and creating. Following weekly faculty-led lectures, student groups identified research questions, analyzed literature, presented data, critiqued peer presentations, and created infographics for the public. Results We aimed to maintain quality and interactiveness despite challenges posed by our timeframe, the evolving COVID-19 literature, and the virtual setting. We recruited frontline faculty and designed the course to facilitate discussion, thereby promoting real-time exploration of public health and clinical challenges. Encouraging student participation, we incorporated group synthesis sessions and instructed use of video, hand-raising, and chat features. In a survey administered at the end of the first week, 85.7% (18/21) of students strongly agreed or agreed that small group presentations successfully enabled synthesis of new and emerging data. Among the 29 enrolled students, 82.8% (24/29) of students completed final course evaluations, with 87.5% (21/24) agreeing that the learning activities “usually” or “always” helped meet the learning objectives identified at the beginning of the course. The course was rated as “excellent” or “very good” by 83.3% (20/24) of students. Conclusion Lessons learned include providing students with increased direction on critically reviewing peer presentations and imparting guidance on best practices for data synthesis. This course model will be disseminated throughout our institution and beyond to address challenges in remote learning and to serve as a paradigm during future health crises. Disclosures All Authors: No reported disclosures

Refining Large Group Presentations

SIG Bulletin ◽  
1984 ◽  
Vol 1 (1) ◽  
pp. 12-13
Author(s):  
Molly Brown
Keyword(s):  
Large Group ◽  
Group Presentations

Zero-Divisors, Torsion Elements, and Unions of Annihilators

2014 ◽  
Vol 43 (1) ◽  
pp. 76-83 ◽  
Author(s):  
D. D. Anderson ◽  
Sangmin Chun
Keyword(s):  
Zero Divisors
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