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

1st Edition - January 1, 1970
Editor: John Leech
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 5 9 4 2 - 3

Computational Problems in Abstract Algebra provides information pertinent to the application of computers to abstract algebra. This book discusses combinatorial problems dealing… Read more

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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.

Foreword

Preface

Investigations of Groups on Computers

Coset Enumeration

Some Examples Using Coset Enumeration

Defining Relations for Subgroups of Finite Index of Groups with a Finite Presentation

Nielsen Transformations

Calculation with the Elements of a Finite Group Given by Generators and Defining Relations

On a Program for the Determination of the Automorphism Group of a Finite Group

A Computational Method for Determining The Automorphism Group of a Finite Solvable Group

Combinatorial Construction by Computer of the Set of All Subgroups of a Finite Group by Composition of Partial Sets of Its Subgroups

A Program for the Drawing of Lattices

The Construction of the Character Table of a Finite Group from Generators and Relations

A Program for the Calculation of Characters and Representations of Finite Groups

The Characters of the Weyl Group E8

On Some Applications of Group-Theoretical Programs to the Derivation of the Crystal Classes of R4

A Search for Simple Groups of Order Less than One Million

Computational Methods in the Study of Permutation Groups

An Algorithm Related to the Restricted Burnside Group of Prime Exponent

A Module-Theoretic Computation Related to the Burnside Problem

Some Combinatorial and Symbol Manipulation Programs in Group Theory

The Computation of Irreducible Representations of Finite Groups of Order 2n, N ≤ 6

Some Examples of Man–Machine Interaction in the Solution of Mathematical Problems

Construction and Analysis of Non-Equivalent Finite Semigroups

Some Contributions of Computation to Semigroups and Groupoids

Simple Word Problems in Universal Algebras

The Application of Computers to Research in Non-Associative Algebras

Identities in Jordan Algebras

On Property D Neofields and Some Problems concerning Orthogonal Latin Squares

A Projective Configuration

The Uses of Computers in Galois Theory

An Enumeration of Knots and Links, and Some of Their Algebraic Properties

Computations in Knot Theory

Computer Experiments on Sequences Which Form Integral Bases

Application of Computer to Algebraic Topology on Some Bicomplex Manifolds

A Real Root Calculus

Some Computational Problems and Methods Related to Invariant Factors and Control Theory

List of Participants