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Presentations of Groups

1997-05-15 Mathematics
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Release : 1997-05-15
Genre : Mathematics
Kind : eBook
Book Rating : 422/5 ( reviews)

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Book Synopsis Presentations of Groups by : D. L. Johnson

Download or read book Presentations of Groups written by D. L. Johnson. This book was released on 1997-05-15. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied.This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.

Topics in the Theory of Group Presentations

1980-07-31 Mathematics
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Release : 1980-07-31
Genre : Mathematics
Kind : eBook
Book Rating : 086/5 ( reviews)

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Book Synopsis Topics in the Theory of Group Presentations by : D. L. Johnson

Download or read book Topics in the Theory of Group Presentations written by D. L. Johnson. This book was released on 1980-07-31. Available in PDF, EPUB and Kindle. Book excerpt: These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises.

Combinatorial Group Theory

2004-01-01 Mathematics
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Release : 2004-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 309/5 ( reviews)

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Book Synopsis Combinatorial Group Theory by : Wilhelm Magnus

Download or read book Combinatorial Group Theory written by Wilhelm Magnus. This book was released on 2004-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This seminal, much-cited account begins with a fairly elementary exposition of basic concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commutator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; and more. Second, revised 1976 edition.

The Bounded and Precise Word Problems for Presentations of Groups

2020-05-13 Education
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Release : 2020-05-13
Genre : Education
Kind : eBook
Book Rating : 438/5 ( reviews)

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Book Synopsis The Bounded and Precise Word Problems for Presentations of Groups by : S. V. Ivanov

Download or read book The Bounded and Precise Word Problems for Presentations of Groups written by S. V. Ivanov. This book was released on 2020-05-13. Available in PDF, EPUB and Kindle. Book excerpt: The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.

Visual Group Theory

2021-06-08 Education
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Release : 2021-06-08
Genre : Education
Kind : eBook
Book Rating : 330/5 ( reviews)

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Book Synopsis Visual Group Theory by : Nathan Carter

Download or read book Visual Group Theory written by Nathan Carter. This book was released on 2021-06-08. Available in PDF, EPUB and Kindle. Book excerpt: Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.

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