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Symmetric Generation of Groups With Applications to Many of the Sporadic Finite Simple Groups 1st Edition by Robert Curtis ISBN 052185721X 9780521857215

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Symmetric Generation of Groups With Applications to Many of the Sporadic Finite Simple Groups Robert Curtis Digital Instant Download

Author(s): Robert Curtis
ISBN(s): 9780521857215, 052185721X
Edition: Illustrated
File Details: PDF, 2.20 MB
Year: 2007
Language: english
SKU: EB-43108670 Category: Tag:

Symmetric Generation of Groups With Applications to Many of the Sporadic Finite Simple Groups 1st Edition by Robert Curtis – Ebook PDF Instant Download/Delivery: 052185721X, 9780521857215
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ISBN 10: 052185721X 
ISBN 13: 9780521857215
Author: Robert Curtis

Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups. But gaining familiarity with these groups presents problems for two reasons. Firstly, they were discovered in many different ways, so to understand their constructions in depth one needs to study lots of different techniques. Secondly, since each of them is in a sense recording some exceptional symmetry in spaces of certain dimensions, they are by their nature highly complicated objects with a rich underlying combinatorial structure. Motivated by initial results which showed that the Mathieu groups can be generated by highly symmetrical sets of elements, which themselves have a natural geometric definition, the author develops from scratch the notion of symmetric generation. He exploits this technique by using it to define and construct many of the sporadic simple groups including all the Janko groups and the Higman-Sims group. For researchers and postgraduates.

Symmetric Generation of Groups With Applications to Many of the Sporadic Finite Simple Groups 1st Table of contents:

  • Introduction

    • Overview of symmetric generation

    • Motivation and scope

    • Summary of sporadic finite simple groups

  • Preliminaries and Background

    • Group theory basics

    • Definitions related to symmetric generation

    • Important theorems and prior results

  • Symmetric Generation: Concepts and Methods

    • Definition and construction of symmetric generators

    • Properties of symmetric generating sets

    • Methods for proving generation

  • Symmetric Presentations of Finite Groups

    • Techniques for symmetric presentations

    • Examples and illustrative cases

    • Algorithmic approaches

  • Applications to Sporadic Simple Groups

    • Overview of sporadic groups

    • Specific symmetric generations for many sporadic groups

    • Case studies (e.g., Mathieu groups, Janko groups)

  • Computational Techniques and Implementations

    • Computational group theory tools

    • Software implementations

    • Algorithms for verification

  • Further Developments and Open Problems

    • Extensions of symmetric generation

    • Connections to other areas of mathematics

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Tags: Robert Curtis, Symmetric Generation, , Sporadic Finite