Infinite Group Theory From The Past To The Future

The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest. Contents: Groups with the Weak Minimal Condition on Non-Permutable Subgroups (Laxmi K Chatuat and Martyn R Dixon)A Survey: Shamir Threshold Scheme and Its Enhancements (Chi Sing Chum, Benjamin Fine, and Xiaowen Zhang)The Zappa-Szep Product of Left-Orderable Groups (Fabienne Chouraqui)Totally Disconnected Groups From Baumslag-Solitar Groups (Murray Elder and George Willis)Elementary and Universal Theories of Nonabelian Commutative Transitive and CSA Groups (B Fine, A M Gaglione, and D Spellman)Commutative Transitivity and the CSA Property (Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, and Dennis Spellman)The Universal Theory of Free Burnside Groups of Large Prime Exponent (Anthony M Gaglione, Seymour Lipschutz, and Dennis Spellman)Primitive Curve Lengths on Pairs of Pants (Jane Gilman)Drawing Inferences Under Maximum Entropy From Relational Probabilistic Knowledge Using Group Theory (Gabriele Kern-Isberner, Marco Wilhelm, and Christoph Beierle)On Some Infinite-Dimensional Linear Groups and the Structure of Related Modules (L A Kurdachenko and I Ya Subbotin)On New Analogs of Some Classical Group Theoretical Results in Lie Rings (L A Kurdachenko, A A Pypka and I Ya Subbotin)Log-Space Complexity of the Conjugacy Problem in Wreath Products (Alexei Myasnikov, Svetla Vassileva, and Armin Weiss)Group Presentations, Cayley Graphs and Markov Processes (Peter Olszewski) Readership: Graduate students and researchers in group theory. Keywords: Infinite Group Theory;Combinatorial Group Theory;Geometric Group TheoryReview: Key Features: This book is centered on infinite group theory from a combinatorial and geometric point of view. It also contains material on non-commutative algebraic group-based cryptography

"The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest."--

This is the second volume of a series of books in various aspects of Mathematical Physics. Mathematical Physics has made great strides in recent years, and is rapidly becoming an important dis cipline in its own right. The fact that physical ideas can help create new mathematical theories, and rigorous mathematical theo rems can help to push the limits of physical theories and solve problems is generally acknowledged. We believe that continuous con tacts between mathematicians and physicists and the resulting dialogue and the cross fertilization of ideas is a good thing. This series of studies is published with this goal in mind. The present volume contains contributions which were original ly presented at the Second NATO Advanced Study Institute on Mathe matical Physics held in Istanbul in the Summer of 1972. The main theme was the application of group theoretical methods in general relativity and in particle physics. Modern group theory, in par ticular, the theory of unitary irreducibl~ infinite-dimensional representations of Lie groups is being increasingly important in the formulation and solution of dynamical problems in various bran ches of physics. There is moreover a general trend of approchement of the methods of general relativity and elementary particle physics. We hope it will be useful to present these investigations to a larger audience.

This is a commemoration volume to honor Professor M Veltman on the ocassion of his 60th birthday. It contains articles on Gauge field theories, a subject to which Prof. Veltman has made many important and seminal contributions. Some of the contributions are based on invited talks given at the Conference held in Ann Arbor, Michigan, May 16 – 18 1991. The articles in the book cover a wide range of topics from formal and phenomenological to the experimental aspects of Gauge theories. Contents:Comments on the Occasion of the Symposium Celebrating the Sixtieth Birthday of Martinus Veltman (H Neal)The Largest Time Equation and Long Distance Behavior in Gauge Field Theories (R Akhoury)Top Quark Condensate Models (W A Bardeen)Fast and Reliable Random Numbers for Extensive Monte Carlo Calculations (A Compagner)Large Higgs Mass, Triviality and Asymptotic Freedom (M Consoli)Strong CP Violation and Effective Chiral Lagrangians (E de Rafael)Is Your Weight Gauge Dependent? (B de Wit)Effective Theories and Thresholds in Particle Physics (M K Gaillard)Neutrino Mass Matrices with Minimal Polynomials of Second or Third Degree in the Three Family Model (C Jarlskog)QCD: Some Like It Hot or Why There Have Been Small Bangs (C Korthal-Altes)The Last Ten Years of Radiative Corrections (G Passarino)The Analytic Value of the Atomic Three Electron Correlation Integral with Slater Wave Functions (E Remiddi)Example of Quantum Field Theory Based on Nonlinear Lie Algebra (P van Nieuwenhuizen, K Schoutens & A Sevrin)Tini and the Cosmological Constant (L Susskind)The Veltman Vertex (R Thun)Third Threshold in Weak Interactions? (H Veltman & J J van der Bij)Relation Between the Practical Results of Current Algebra Techniques and the Originating Quark Model (M Veltman)Landau Poles, Violations of Unitarity and a Bound on the Top Quark Mass (F J Yndurain)and other papers Readership: High energy physicists. keywords:

270 Expert contributions on aspects of landslide hazards, encompassing geological modeling and soil and rock mechanics, landslide processes, causes and effects, and damage avoidance and limitation strategies. Reference source for academics and professionals in geo-mechanical and geo-technical engineering, and others involved with research, des

In February 1981, the classification of the finite simple groups (Dl)* was completed,t. * representing one of the most remarkable achievements in the history or mathematics. Involving the combined efforts of several hundred mathematicians from around the world over a period of 30 years, the full proof covered something between 5,000 and 10,000 journal pages, spread over 300 to 500 individual papers. The single result that, more than any other, opened up the field and foreshadowed the vastness of the full classification proof was the celebrated theorem of Walter Feit and John Thompson in 1962, which stated that every finite group of odd order (D2) is solvable (D3)-a statement expressi ble in a single line, yet its proof required a full 255-page issue of the Pacific 10urnal of Mathematics [93]. Soon thereafter, in 1965, came the first new sporadic simple group in over 100 years, the Zvonimir Janko group 1 , to further stimulate the 1 'To make the book as self-contained as possible. we are including definitions of various terms as they occur in the text. However. in order not to disrupt the continuity of the discussion. we have placed them at the end of the Introduction. We denote these definitions by (DI). (D2), (D3). etc.

This book is a festschrift in honor of Professor Anthony Gaglione''s sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.

Why should mathematical logic be grounded on the basis of some formal requirements in the way that it has been developed since its classical emergence as a hybrid field of mathematics and logic in the 19th century or earlier? Contrary to conventional wisdom, the foundation of mathematic logic has been grounded on some false (or dogmatic) assumptions which have much impoverished the pursuit of knowledge. This is not to say that mathematical logic has been useless. Quite on the contrary, it has been quite influential in shaping the way that reality is to be understood in numerous fields of knowledge—by learning from the mathematical study of logic and its reverse, the logical study of mathematics. In the final analysis, the future of mathematical logic will depend on how its foundational crisis is to be resolved, and "the contrastive theory of rationality" (in this book) is to precisely show how and why it can be done by taking a contrastive turn, subject to the constraints imposed upon by "existential dialectic principles" at the ontological level (to avoid any reductionistic fallacy) and other ones (like the perspectives of culture, society, nature, and the mind). The contrastive theory of rationality thus shows a better way to ground mathematical logic (beyond both classical and non-classical logics) for the future advancement of knowledge and, if true, will alter the way of how mathematical logic is to be understood, with its enormous implications for the future of knowledge and its "post-human" fate.