Symmetric Generation of Groups: With Applications to many of the Sporadic Finite Simple Groups

by Robert T. Curtis

Overview

Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups. However, gaining familiarity with these groups presents problems for two reasons. First, they were discovered in many different ways, so to understand their constructions in depth one needs to study lots of different techniques. Second, 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. This volume is suitable for researchers and postgraduates.

Product Details

ISBN-13:	9780521857215
Publisher:	Cambridge University Press
Publication date:	07/05/2007
Series:	Encyclopedia of Mathematics and its Applications , #111
Pages:	332
Product dimensions:	6.50(w) x 9.45(h) x 0.98(d)

About the Author

Robert T. Curtis is Professor of Combinatorial Algebra and Head of Pure Mathematics in the School of Mathematics at the University of Birmingham. He also holds the post of Librarian for the London Mathematical Society.

Table of Contents

Preface; Acknowledgements; Part I. Motivation: 1. The Mathieu group M12; 2. The Mathieu group M24; Part II. Involutory Symmetric Generators: 3. The progenitor; 4. Classical examples; 5. Sporadic simple groups; Part III. Non-involutory Symmetric Generators: 6. The progenitor; 7. Images of these progenitors.