Probabilistic Group Theory, Combinatorics, and Computing

Author: Alla Detinko

Publisher: Springer

ISBN: 9781447148142

Category: Mathematics

Page: 107

View: 924

Probabilistic Group Theory, Combinatorics and Computing is based on lecture courses held at the Fifth de Brún Workshop in Galway, Ireland in April 2011. Each course discusses computational and algorithmic aspects that have recently emerged at the interface of group theory and combinatorics, with a strong focus on probabilistic methods and results. The courses served as a forum for devising new strategic approaches and for discussing the main open problems to be solved in the further development of each area. The book represents a valuable resource for advanced lecture courses. Researchers at all levels are introduced to the main methods and the state-of-the-art, leading up to the very latest developments. One primary aim of the book’s approach and design is to enable postgraduate students to make immediate use of the material presented.
The Spread of Almost Simple Classical Groups

Author: Scott Harper

Publisher: Springer Nature

ISBN: 9783030741006

Category: Mathematics

Page: 154

View: 250

This monograph studies generating sets of almost simple classical groups, by bounding the spread of these groups. Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group, every nontrivial element belongs to a generating pair. Groups with this property are said to be 3/2-generated. Breuer, Guralnick and Kantor conjectured that a finite group is 3/2-generated if and only if every proper quotient is cyclic. We prove a strong version of this conjecture for almost simple classical groups, by bounding the spread of these groups. This involves analysing the automorphisms, fixed point ratios and subgroup structure of almost simple classical groups, so the first half of this monograph is dedicated to these general topics. In particular, we give a general exposition of Shintani descent. This monograph will interest researchers in group generation, but the opening chapters also serve as a general introduction to the almost simple classical groups.
Finite Simple Groups: Thirty Years of the Atlas and Beyond

Author: Manjul Bhargava

Publisher: American Mathematical Soc.

ISBN: 9781470436780

Category: Atlas of finite groups

Page: 229

View: 212

Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.
Applying the Classification of Finite Simple Groups: A User’s Guide

Author: Stephen D. Smith

Publisher: American Mathematical Soc.

ISBN: 9781470442910

Category: Finite simple groups

Page: 231

View: 741

Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
Intelligent Computer Mathematics

Author: Fairouz Kamareddine

Publisher: Springer Nature

ISBN: 9783030810979

Category: Computers

Page: 263

View: 323

This book constitutes the refereed proceedings of the 14th International Conference on Intelligent Computer Mathematics, CICM 2021, held in Timisoara, Romania, in July 2021*. The 12 full papers, 7 system descriptions, 1 system entry, and 3 abstracts of invited papers presented were carefully reviewed and selected from a total of 38 submissions. The papers focus on advances in formalization, automatic theorem proving and learning, search and classification, teaching and geometric reasoning, and logic and systems, among other topics. * The conference was held virtually due to the COVID-19 pandemic.
Groups St. Andrews 1997 in Bath

Author: C. M. Campbell

Publisher: Cambridge University Press

ISBN: 0521655765


Page: 374

View: 220

This two-volume book contains selected papers from the international conference 'Groups St Andrews 1997 in Bath'. The articles cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together with refereed survey and research articles contributed by other conference participants. Proceedings of earlier 'Groups St Andrews' conferences have had a major impact on the development of group theory and these volumes should be equally important.
Infinite Groups: Geometric, Combinatorial and Dynamical Aspects

Author: Laurent Bartholdi

Publisher: Springer Science & Business Media

ISBN: 9783764374471

Category: Mathematics

Page: 416

View: 470

This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics.
Computational Intelligence

Author: Nazmul Siddique

Publisher: John Wiley & Sons

ISBN: 9781118534816

Category: Technology & Engineering

Page: 536

View: 855

Computational Intelligence: Synergies of Fuzzy Logic, NeuralNetworks and Evolutionary Computing presents an introduction tosome of the cutting edge technological paradigms under the umbrellaof computational intelligence. Computational intelligence schemesare investigated with the development of a suitable framework forfuzzy logic, neural networks and evolutionary computing,neuro-fuzzy systems, evolutionary-fuzzy systems and evolutionaryneural systems. Applications to linear and non-linear systems arediscussed with examples. Key features: Covers all the aspects of fuzzy, neural and evolutionaryapproaches with worked out examples, MATLAB® exercises andapplications in each chapter Presents the synergies of technologies of computationalintelligence such as evolutionary fuzzy neural fuzzy andevolutionary neural systems Considers real world problems in the domain of systemsmodelling, control and optimization Contains a foreword written by Lotfi Zadeh Computational Intelligence: Synergies of Fuzzy Logic, NeuralNetworks and Evolutionary Computing is an ideal text for finalyear undergraduate, postgraduate and research students inelectrical, control, computer, industrial and manufacturingengineering.
Combinatorial and Computational Algebra

Author: Kai-Yuen Chan

Publisher: American Mathematical Soc.

ISBN: 9780821819845

Category: Algebra

Page: 318

View: 482

This volume presents articles based on the talks at the International Conference on Combinatorial and Computational Algebra held at the University of Hong Kong (China). The conference was part of the Algebra Program at the Institute of Mathematical Research and the Mathematics Department at the University of Hong Kong. Topics include recent developments in the following areas: combinatorial and computational aspects of group theory, combinatorial and computational aspects of associative and nonassociative algebras, automorphisms of polynomial algebras and the Jacobian conjecture, and combinatorics and coding theory. This volume can serve as a solid introductory guide for advanced graduate students, as well as a rich and up-to-date reference source for contemporary researchers in the field.
Combinatorial and Geometric Group Theory

Author: Oleg Bogopolski

Publisher: Springer Science & Business Media

ISBN: 9783764399115

Category: Mathematics

Page: 315

View: 488

This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.