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
Published on 17. May 2014
412 pages
978-1-4831-5942-3 (ISBN)
Description
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.
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Content
ForewordPrefaceInvestigations of Groups on ComputersCoset EnumerationSome Examples Using Coset EnumerationDefining Relations for Subgroups of Finite Index of Groups with a Finite PresentationNielsen TransformationsCalculation with the Elements of a Finite Group Given by Generators and Defining RelationsOn a Program for the Determination of the Automorphism Group of a Finite GroupA Computational Method for Determining The Automorphism Group of a Finite Solvable GroupCombinatorial Construction by Computer of the Set of All Subgroups of a Finite Group by Composition of Partial Sets of Its SubgroupsA Program for the Drawing of LatticesThe Construction of the Character Table of a Finite Group from Generators and RelationsA Program for the Calculation of Characters and Representations of Finite GroupsThe Characters of the Weyl Group E8On Some Applications of Group-Theoretical Programs to the Derivation of the Crystal Classes of R4A Search for Simple Groups of Order Less than One MillionComputational Methods in the Study of Permutation GroupsAn Algorithm Related to the Restricted Burnside Group of Prime ExponentA Module-Theoretic Computation Related to the Burnside ProblemSome Combinatorial and Symbol Manipulation Programs in Group TheoryThe Computation of Irreducible Representations of Finite Groups of Order 2n, N = 6Some Examples of Man-Machine Interaction in the Solution of Mathematical ProblemsConstruction and Analysis of Non-Equivalent Finite SemigroupsSome Contributions of Computation to Semigroups and GroupoidsSimple Word Problems in Universal AlgebrasThe Application of Computers to Research in Non-Associative AlgebrasIdentities in Jordan AlgebrasOn Property D Neofields and Some Problems concerning Orthogonal Latin SquaresA Projective ConfigurationThe Uses of Computers in Galois TheoryAn Enumeration of Knots and Links, and Some of Their Algebraic PropertiesComputations in Knot TheoryComputer Experiments on Sequences Which Form Integral BasesApplication of Computer to Algebraic Topology on Some Bicomplex ManifoldsA Real Root CalculusSome Computational Problems and Methods Related to Invariant Factors and Control TheoryList of Participants
