Groups, Languages and Automata
£79.99
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: Hardback
 isbn: 9781107152359
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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.
Read more 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
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
See more 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 selfcontained condensation of hundreds of individual articles. It will serve as a valuable onestop resource for both researchers and students.' Eric M. Freden, MathSciNet
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×Product details
 Date Published: February 2017
 format: Hardback
 isbn: 9781107152359
 length: 306 pages
 dimensions: 235 x 160 x 21 mm
 weight: 0.57kg
 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 coset systems
9. Automata Groups
Part III. The Word Problem:
10. Solubility of the word problem
11. Contextfree and onecounter word problems
12. Contextsensitive word problems
13. Word problems in other language classes
14. The coword problem and the conjugacy problem
References
Index of notation
Index of names
Index of topics and terminology.
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