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
- Imprint: Pergamon
- Editor: John Leech
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 1 - 2 7 0 0 - 2
- 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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Request a sales quoteComputational 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
- Edition: 1
- Published: January 1, 1970
- No. of pages (eBook): 412
- Imprint: Pergamon
- Language: English
- Paperback ISBN: 9781483127002
- eBook ISBN: 9781483159423
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