Finitely Presented Infinite Simple Groups
Author: Graham Higman
Publisher:
Published: 1974
Total Pages: 96
ISBN-13:
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Author: Graham Higman
Publisher:
Published: 1974
Total Pages: 96
ISBN-13:
DOWNLOAD EBOOKAuthor:
Publisher:
Published: 1981
Total Pages: 154
ISBN-13:
DOWNLOAD EBOOKAuthor: E. A. Scott
Publisher:
Published: 1989
Total Pages: 31
ISBN-13:
DOWNLOAD EBOOKAuthor: Graham Higman
Publisher:
Published: 1973
Total Pages: 29
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DOWNLOAD EBOOKAuthor: Laurent Bartholdi
Publisher: Springer Science & Business Media
Published: 2006-03-28
Total Pages: 419
ISBN-13: 3764374470
DOWNLOAD EBOOKThis book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics.
Author: Pierre de la Harpe
Publisher: University of Chicago Press
Published: 2000-09-15
Total Pages: 348
ISBN-13: 9780226317212
DOWNLOAD EBOOKIn this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.
Author: Volodymyr Nekrashevych
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 248
ISBN-13: 0821838318
DOWNLOAD EBOOKSelf-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.
Author: Charles C. Sims
Publisher: Cambridge University Press
Published: 1994-01-28
Total Pages: 624
ISBN-13: 0521432138
DOWNLOAD EBOOKResearch 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.
Author: Gilbert Baumslag
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 235
ISBN-13: 1461397308
DOWNLOAD EBOOKThe papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics.
Author: E. A. Scott
Publisher:
Published: 1981
Total Pages:
ISBN-13:
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