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Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications, Series Number 48) - Softcover
Synopsis
The book describes methods for working with elements, subgroups, and quotient groups of a finitely presented group. The author emphasizes the connection with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, from computational number theory, and from computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms are used to study the Abelian quotients of a finitely presented group. The work of Baumslag, Cannonito, and Miller on computing non-Abelian polycyclic quotients is described as a generalization of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group.
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Book Description
It is a comprehensive text presenting the fundamental algorithmic ideas which have been developed to compute with finitely presented groups, discussing techniques for computing with finitely presented groups which are infinite, or at least not obviously finite, and describing methods for working with elements, subgroups, and quotient groups of a finitely presented group.
Review
"this book is a very interesting treatment of the computational aspects of combinatorial group theory. It is well-written, nicely illustrating the algorithms presented with many examples. Also, some remarks on the history of the field are included. In adition, many exercises are provided throughout...this is a very valuable book that is well-suited as a textbook for a graduate course on computational group theory. It addresses students of mahtematics and of computer science alike, providing the necessary background for both. In addition, this book will be of good use as a reference source for computational aspects of combinatorial group theory." Friedrich Otto, Mathematical Reviews
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Computation with Finitely Presented Groups
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Cambridge University Press, 2010
ISBN 10: 0521135079
ISBN 13: 9780521135078
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Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications, Series Number 48)
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ISBN 10: 0521135079
ISBN 13: 9780521135078
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Computation With Finitely Presented Groups (Paperback)
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ISBN 10: 0521135079
ISBN 13: 9780521135078
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Paperback. Condition: new. Paperback. The book describes methods for working with elements, subgroups, and quotient groups of a finitely presented group. The author emphasizes the connection with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, from computational number theory, and from computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms are used to study the Abelian quotients of a finitely presented group. The work of Baumslag, Cannonito, and Miller on computing non-Abelian polycyclic quotients is described as a generalization of Buchberger's Grobner basis methods to right ideals in the integral group ring of a polycyclic group. This book describes the basic algorithmic ideas behind accepted methods for computing with finitely presented groups. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780521135078
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Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications, Series Number 48)
Published by
Cambridge University Press, 2010
ISBN 10: 0521135079
ISBN 13: 9780521135078
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Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications)
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ISBN 10: 0521135079
ISBN 13: 9780521135078
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Computation with Finitely Presented Groups
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Computation with Finitely Presented Groups
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Computation with Finitely Presented Groups
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Computation With Finitely Presented Groups (Paperback)
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Cambridge University Press, Cambridge, 2010
ISBN 10: 0521135079
ISBN 13: 9780521135078
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Paperback. Condition: new. Paperback. The book describes methods for working with elements, subgroups, and quotient groups of a finitely presented group. The author emphasizes the connection with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, from computational number theory, and from computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms are used to study the Abelian quotients of a finitely presented group. The work of Baumslag, Cannonito, and Miller on computing non-Abelian polycyclic quotients is described as a generalization of Buchberger's Grobner basis methods to right ideals in the integral group ring of a polycyclic group. This book describes the basic algorithmic ideas behind accepted methods for computing with finitely presented groups. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9780521135078
Quantity: 1 available