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Computation with Finitely Presented Groups

1994-01-28 Mathematics
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Release : 1994-01-28
Genre : Mathematics
Kind : eBook
Book Rating : 138/5 ( reviews)

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Book Synopsis Computation with Finitely Presented Groups by : Charles C. Sims

Download or read book Computation with Finitely Presented Groups written by Charles C. Sims. This book was released on 1994-01-28. Available in PDF, EPUB and Kindle. Book excerpt: Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.

Self-Similar Groups

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 318/5 ( reviews)

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Book Synopsis Self-Similar Groups by : Volodymyr Nekrashevych

Download or read book Self-Similar Groups written by Volodymyr Nekrashevych. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. This connection is established through the central topics of the book, which are the notions of the iterated monodromy group and limit space. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. In particular, it is shown that Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties can appear not just as isolated examples, but as naturally defined iterated monodromy groups of rational functions. The book offers important, new mathematics that will open new avenues of research in group theory and dynamical systems. It is intended to be accessible to a wide readership of professional mathematicians.

Cellular Automata and Groups

2010-08-24 Computers
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Release : 2010-08-24
Genre : Computers
Kind : eBook
Book Rating : 343/5 ( reviews)

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Book Synopsis Cellular Automata and Groups by : Tullio Ceccherini-Silberstein

Download or read book Cellular Automata and Groups written by Tullio Ceccherini-Silberstein. This book was released on 2010-08-24. Available in PDF, EPUB and Kindle. Book excerpt: Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.

Finitely Presented Groups

2024-10-07 Mathematics
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Release : 2024-10-07
Genre : Mathematics
Kind : eBook
Book Rating : 570/5 ( reviews)

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Book Synopsis Finitely Presented Groups by : Volker Diekert

Download or read book Finitely Presented Groups written by Volker Diekert. This book was released on 2024-10-07. Available in PDF, EPUB and Kindle. Book excerpt: This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.

Finitely Presented Infinite Simple Groups

1974 Mathematics
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Release : 1974
Genre : Mathematics
Kind : eBook
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Book Synopsis Finitely Presented Infinite Simple Groups by : Graham Higman

Download or read book Finitely Presented Infinite Simple Groups written by Graham Higman. This book was released on 1974. Available in PDF, EPUB and Kindle. Book excerpt:

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