The Art of Working with the Mathieu Group M24

Author: Robert T. Curtis Series: Cambridge Tracts in Mathematics

Hardcover

An accessible approach to working with the important group M24, demonstrating how the methods introduced are used in other contexts.

The group M24 leads to the Leech lattice, leading to the largest Conway group, and thence to the Monster group. Every mathematician has heard of these structures; balancing theory and computation, the book explains where they come from, in a manner accessible to advanced undergraduates, research students and senior researchers.

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Summary

An accessible approach to working with the important group M24, demonstrating how the methods introduced are used in other contexts.

Description

The Leech lattice Λ, the Conway group ∙O, and the Monster group M are immensely famous structures. They each grow out of the Mathieu group M24 and its underlying combinatorial structure, and play an important role in various branches of mathematics and in theoretical physics. Written by an expert in the field, this book provides a new generation of mathematicians with the intimate knowledge of M24 needed to understand these beautiful objects, and many others. It starts by exploring Steiner systems, before introducing the Miracle Octad Generator (MOG) as a device for working with the Steiner system S(5,8,24). Emphasizing how theoretical and computational approaches complement one another, the author describes how familiarity with M24 leads to the concept of 'symmetric generation' of groups. The final chapter brings together the various strands of the book to produce a nested chain of groups culminating in the largest Conway simple group Co1.

About the Author

Robert T. Curtis is Emeritus Professor of Combinatorial Algebra at the University of Birmingham. He is the author of 'Symmetric Generation of Groups' (2007) and co-author of 'An Atlas of Finite Groups' (1985). He was the London Mathematical Society Librarian from 2003 to 2007 and Treasurer from 2011 to 2020.