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Author: Alexander Lubotzky
Publisher: Birkhäuser
ISBN: 3034889658
Category : Mathematics
Languages : en
Pages : 463
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Book Description
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and Strong Approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'.
Author: Alexander Lubotzky
Publisher: Birkhäuser
ISBN: 3034889658
Category : Mathematics
Languages : en
Pages : 463
Get Book Here
Book Description
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and Strong Approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'.
Author: Marcus du Sautoy
Publisher: Springer Science & Business Media
ISBN: 9780817641719
Category : Mathematics
Languages : en
Pages : 444
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Book Description
A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts.
Author: B. Sury
Publisher: Springer
ISBN: 9386279193
Category : Mathematics
Languages : en
Pages : 315
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Book Description
Author: Francesco Giovanni
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110810387
Category : Mathematics
Languages : en
Pages : 356
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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author: Stephen D. Smith
Publisher: American Mathematical Soc.
ISBN: 1470442914
Category : Mathematics
Languages : en
Pages : 248
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Book Description
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.
Author: Tullio Ceccherini-Silberstein
Publisher: Cambridge University Press
ISBN: 1316604403
Category : Mathematics
Languages : en
Pages : 539
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Book Description
An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.
Author: Minnesota Academy of Science (1932- ). Meeting
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 814
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Book Description
Author: Minnesota Academy of Science
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 826
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Book Description
Author: Kate Kennedy
Publisher: Corwin Press
ISBN: 1412996333
Category : Education
Languages : en
Pages : 201
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Book Description
Value-added is the most robust, statistically significant method for connecting teachers to students. In other words, value-added analysis links teachers to students and, for the very first time, allows educators to see the amount of growth they are facilitating with students. Built around the value-added analysis professional development work of Battelle for Kids, this book for district and school leaders prepares educators to understand and implement value-added analysis in order to ensure that all students are achieving and progressing. By providing a user-friendly, five-step implementation process along with success stories of schools, teachers, and students as well as strategies, samples, and tools, this book will equip educators to use value-added analysis to help accelerate student progress. It is written to inform readers about what value-added analysis is and to help them utilize value-added information in a classroom and/or school setting.
Author: Johannes Fürnkranz
Publisher: Springer
ISBN: 3540460489
Category : Computers
Languages : en
Pages : 681
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Book Description
This book constitutes the refereed proceedings of the 10th European Conference on Principles and Practice of Knowledge Discovery in Databases, PKDD 2006. The book presents 36 revised full papers and 26 revised short papers together with abstracts of 5 invited talks, carefully reviewed and selected from 564 papers submitted. The papers offer a wealth of new results in knowledge discovery in databases and address all current issues in the area.
