Computational Problems in Abstract Algebra

Proceedings of a Conference Held at Oxford Under the Auspices of the Science Research Council Atlas Computer Laboratory, 29th August to 2nd September 1967

John Leech

• Publisher: Pergamon
• Year: 2014
• Print ISBN:
  9780080129754
• eBook ISBN:
  9781483159423
• Topic: Mathematics
• Subtopic: Group Theory
• Index: Mathematics

Computational Problems in Abstract Algebra provides information pertinent to the application of computers to abstract algebra. This book discusses combinatorial problems dealing with things like generation of permutations, projective planes, orthogonal latin squares, graphs, difference sets, block designs, and Hadamard matrices. Comprised of 35 chapters, this book begins with an overview of the methods utilized in and results obtained by programs for the investigation of groups. This text then examines the method for establishing the order of a finite group defined by a set of relations satisfied by its generators. Other chapters describe the modification of the Todd–Coxeter coset enumeration process. This book discusses as well the difficulties that arise with multiplication and inverting programs, and of some ways to avoid or overcome them. The final chapter deals with the computational problems related to invariant factors in linear algebra. Mathematicians as well as students of algebra will find this book useful.

Table of contents

• Front Cover
• Computational Problems in Abstract Algebra
• Copyright Page
• Table of Contents
• Foreword
• Preface
• Chapter 1. Investigations of groups on computers
• Chapter 2. Coset enumeration
• Chapter 3. Some examples using toset enumeration
• Chapter 4. Defining relations for subgroups of finite index of groups with a finite presentation
• Chapter 5. Nielsen transformations
• Chapter 6. Calculation with the elements of a finite group given by generators and defining relations
• Chapter 7. On a programme for the determination of the automorphism group of a finite group
• Chapter 8. A computational method for determining the automorphism group of a finite solvable group
• Chapter 9. Combinatorial construction by computer of the set of all subgroups of a finite group by composition of partial sets of its subgroups
• Chapter 10. A programme for the drawing of lattices
• Chapter 11. The construction of the character table of a finite group from generators and relations
• Chapter 12. A programme for the calculation of characters and representations of finite groups
• Chapter 13. The characters of the Weyl group E8
• Chapter 14. On some applications of group-theoretical programmes to the derivation of the crystal classes of R4
• Chapter 15. A search for simple groups of order less than one millions
• Chapter 16. Computational methods in the study of permutation groupst
• Chapter 17. An algorithm related to the restricted Burnside group of prime exponent
• Chapter 18. A module-theoretic computation related to the Burnside problem
• Chapter 19. Some combinatorial and symbol manipulation programs in group theory
• Chapter 20. The computation of irreducible representations of finite groups of order 2n, n< 6t
• Chapter 21. Some examples of man—machine interaction in the solution of mathematical problems
• Chapter 22. Construction and analysis of non-equivalent finite semigroups
• Chapter 23. Some contributions of computation to semigroups and groupoidst
• Chapter 24. Simple Word Problems in Universal Algebrast
• Chapter 25. The application of computers to research innon-associative algebras
• Chapter 26. Identities in Jordan algebras
• Chapter 27. On property D neofields and some problems concerning orthogonal latin squares
• Chapter 28. A projective configuration
• Chapter 29. The uses of computers in Galois theory
• Chapter 30. An enumeration of knots and links, and some of their algebraic properties
• Chapter 31. Computations in knot theory
• Chapter 32. Computer experiments on sequences which formintegral bases
• Chapter 33. Application of computer to algebraic topology on some bicomplex manifoldst
• Chapter 34. A real root calculus
• Chapter 35. Some computational problems and methods related to invariant factors and control theoryt
• List of participants