Free product

About: Free product is a research topic. Over the lifetime, 1844 publications have been published within this topic receiving 39590 citations.

The algebraic theory of semigroups

Abstract: This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into the theories of minimal ideals in a semi group, inverse semi groups, simple semi groups, congruences on a semi group, and the embedding of a semi group in a group. Among the more important recent developments of which an extended treatment is presented are B. M. Sain's theory of the representations of an arbitrary semi group by partial one-to-one transformations of a set, L. Redei's theory of finitely generated commutative semi groups, J. M. Howie's theory of amalgamated free products of semi groups, and E. J. Tully's theory of representations of a semi group by transformations of a set. Also a full account is given of Malcev's theory of the congruences on a full transformation semi group.

Combinatorial Group Theory

Abstract: Chapter I. Free Groups and Their Subgroups 1. Introduction 2. Nielsen's Method 3. Subgroups of Free Groups 4. Automorphisms of Free Groups 5. Stabilizers in Aut(F) 6. Equations over Groups 7. Quadratic sets of Word 8. Equations in Free Groups 9. Abstract Lenght Functions 10. Representations of Free Groups 11. Free Pruducts with Amalgamation Chapter II. Generators and Relations 1. Introduction 2. Finite Presentations 3. Fox Calculus, Relation Matrices, Connections with Cohomology 4. The Reidemeister-Schreier Method 5. Groups with a Single Defining Relator 6. Magnus' Treatment of One-Relator Groups Chapter III. Geometric Methods 1. Introduction 2. Complexes 3. Covering Maps 4. Cayley Complexes 5. Planar Caley Complexes 6. F-Groups Continued 7. Fuchsian Complexes 8. Planar Groups with Reflections 9. Singular Subcomplexes 10. Sherical Diagrams 11. Aspherical Groups 12. Coset Diagrams and Permutation Representations 13. Behr Graphs Chpter IV. Free Products and HNN Extensions 1. Free Products 2. Higman-Neumann-Neumann Extensions and Free Products with Amalgamation 3. Some Embedding Theorems 4. Some Decision Problems 5. One-Relator Groups 6. Bipolar Structures 7. The Higman Embedding Theorem 8. Algebraically Closed Groups Chapter V. Small Cancellation Theory 1. Diagrams 2. The Small Cancellation Hypotheses 3. The Basic Formulas 4. Dehn's Algorithm and Greendlinger's Lemma 5. The Conjugacy Problem 6. The Word Problem 7. The Cunjugacy Problme 8. Applications to Knot Groups 9. The Theory over Free Products 10. Small Cancellation Products 11. Small Cancellation Theory over free Products with Amalgamation and HNN Extensions Bibliography Index of Names Subject Index

On hyperbolic groups

Abstract: We prove that a δ-hyperbolic group for δ < 1 2 is a free product F ∗ G1 ∗ . . . ∗Gn where F is a free group of finite rank and each Gi is a finite group.

Lectures on the Combinatorics of Free Probability

Abstract: Part I. Basic Concepts: 1. Non-commutative probability spaces and distributions 2. A case study of non-normal distribution 3. C*-probability spaces 4. Non-commutative joint distributions 5. Definition and basic properties of free independence 6. Free product of *-probability spaces 7. Free product of C*-probability spaces Part II. Cumulants: 8. Motivation: free central limit theorem 9. Basic combinatorics I: non-crossing partitions 10. Basic Combinatorics II: Mobius inversion 11. Free cumulants: definition and basic properties 12. Sums of free random variables 13. More about limit theorems and infinitely divisible distributions 14. Products of free random variables 15. R-diagonal elements Part III. Transforms and Models: 16. The R-transform 17. The operation of boxed convolution 18. More on the 1-dimensional boxed convolution 19. The free commutator 20. R-cyclic matrices 21. The full Fock space model for the R-transform 22. Gaussian Random Matrices 23. Unitary Random Matrices Notes and Comments Bibliography Index.