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Look Inside Groups, Languages and Automata

Groups, Languages and Automata

Groups, Languages and Automata

Part of London Mathematical Society Student Texts

Authors:
Derek F. Holt, University of Warwick
Sarah Rees, University of Newcastle upon Tyne
Claas E. Röver, National University of Ireland, Galway

Date Published: February 2017
availability: Available
format: Paperback
isbn: 9781316606520

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Description

About the Authors

Fascinating connections exist between group theory and automata theory, and a wide variety of them are discussed in this text. Automata can be used in group theory to encode complexity, to represent aspects of underlying geometry on a space on which a group acts, and to provide efficient algorithms for practical computation. There are also many applications in geometric group theory. The authors provide background material in each of these related areas, as well as exploring the connections along a number of strands that lead to the forefront of current research in geometric group theory. Examples studied in detail include hyperbolic groups, Euclidean groups, braid groups, Coxeter groups, Artin groups, and automata groups such as the Grigorchuk group. This book will be a convenient reference point for established mathematicians who need to understand background material for applications, and can serve as a textbook for research students in (geometric) group theory.
- Can be used as a primary text for new postgraduates
- Contains detailed coverage of many of the interesting examples arising in geometric group theory, including hyperbolic groups, manifold groups, braid groups, Coxeter groups, and more
- Includes all the necessary background material, with sketch proofs or exercises for the more important results on which the applications to group theory depend
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Reviews & endorsements
'The authors study how automata can be used to determine whether a group has a solvable word problem or not. They give detailed explanations on how automata can be used in group theory to encode complexity, to represent certain aspects of the underlying geometry of a space on which a group acts, its relation to hyperbolic groups … it will convince the reader of the beauty and richness of Group Theory.' Charles Traina, MAA Reviews
'There are copious references and separate indices for notation, subjects, and names of earlier researchers. In summary, this text (written by three experts on the subjects) is a mostly self-contained condensation of hundreds of individual articles. It will serve as a valuable one-stop resource for both researchers and students.' Eric M. Freden, MathSciNet
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Product details
- Date Published: February 2017
- format: Paperback
- isbn: 9781316606520
- length: 306 pages
- dimensions: 227 x 152 x 18 mm
- weight: 0.45kg
- contains: 35 b/w illus. 25 exercises
- availability: Available
Table of Contents
Preface
Part I. Introduction:
1. Group theory
2. Formal languages and automata theory
3. Introduction to the word problem
Part II. Finite State Automata and Groups:
4. Rewriting systems
5. Automatic groups
6. Hyperbolic groups
7. Geodesics
8. Subgroups and co-set systems
9. Automata Groups
Part III. The Word Problem:
10. Solubility of the word problem
11. Context-free and one-counter word problems
12. Context-sensitive word problems
13. Word problems in other language classes
14. The co-word problem and the conjugacy problem
References
Index of notation
Index of names
Index of topics and terminology.
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Authors
Derek F. Holt, University of Warwick
Derek F. Holt is a professor of mathematics at the University of Warwick. He authored the successful Handbook of Computational Group Theory, which has now become the standard text in the subject, and he co-authored The Maximal Subgroups of Low-Dimensional Groups (with John N. Bray and Colva M. Roney-Dougal, Cambridge, 2013). Holt was also one of five co-authors of the seminal book Word Processing in Groups (1992) on the theory of automatic groups, and has contributed mathematical software to the Magma and GAP systems. In 1981, he was awarded the London Mathematical Society Junior Whitehead Prize.
Sarah Rees, University of Newcastle upon Tyne
Sarah Rees is a professor of pure mathematics at the University of Newcastle upon Tyne. She is an active researcher in the fields covered in this book, and has supervised a number of graduate students in this area.
Claas E. Röver, National University of Ireland, Galway
Claas E. Röver is a lecturer in mathematics at the National University of Ireland, Galway. He began researching the topics covered in this book during a post-doctoral position in Newcastle and has since contributed to the rapid development of this area of mathematics.

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