The Mathieu Groups

A. A. Ivanov

• Publisher: Cambridge University Press
• Year: 2018
• Print ISBN: 9781108429788
• eBook ISBN: 9781108556798
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

The Mathieu groups have many fascinating and unusual characteristics and have been studied at length since their discovery. This book provides a unique, geometric perspective on these groups. The amalgam method is explained and used to construct M24, enabling readers to learn the method through its application to a familiar example. The same method is then used to construct, among others, the octad graph, the Witt design and the Golay code. This book also provides a systematic account of 'small groups', and serves as a useful reference for the Mathieu groups. The material is presented in such a way that it guides the reader smoothly and intuitively through the process, leading to a deeper understanding of the topic.

Table of contents

• Cover
• Half-title page
• Series page
• Title page
• Copyright page
• Dedication
• Contents
• Preface
• 1 The Mathieu Group M[sub(24)] As We Knew It
• 2 The Amalgam Method
• 3 L[sub(4)](2) in Two Incarnations and L[sub(3)](4)
• 4 From L[sub(5)](2) to the Mathieu Amalgam
• 5 M[sub(24)] As Universal Completion
• 6 Maximal Subgroups
• 7 The 45-Representation of M[sub(24)]
• 8 The Held Group
• 9 The Inevitability of Mathieu Groups
• 10 Locally Projective Graphs and Amalgams
• References
• Index