Ever-Evolving Groups
An Introduction to Modern Finite Group Theory
Series: Algebra and Applications; 32;
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31 768 Ft
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Product details:
- Publisher Springer
- Date of Publication 1 June 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783031890109
- Binding Hardback
- No. of pages339 pages
- Size 235x155 mm
- Language English
- Illustrations 1 Illustrations, color 700
Categories
Short description:
This book presents an original approach to the theory of finite groups, placing finite sporadic groups on an equal footing. It provides a nearly comprehensive overview of developments in the study of sporadic groups since the classification of finite simple groups was completed.
Authored by one of the key contributors to these developments, a major theme of the book is the growing role that geometry has played in this story in the form of diagram geometries, amalgams, graph theory and “pushing up”. The chapters interweave various ideas and techniques applicable to all sporadic groups. Many of the results presented—several due to the author and collaborators—appear in book form for the first time. While much of the book describes developments from recent decades, it also includes significant new material, notably on the enigmatic Thompson group and the Monster. The final chapter explores connections to Majorana algebras and discusses some remarkable conjectures.
A valuable addition to the literature on finite simple groups, this book will appeal to a wide audience, from advanced graduate students to researchers in group theory, combinatorics, finite geometry, coding theory, graph theory, and other mathematical fields that use group theory to study symmetries and structures.
Long description:
This book presents an original approach to the theory of finite groups, placing finite sporadic groups on an equal footing. It provides a nearly comprehensive overview of developments in the study of sporadic groups since the classification of finite simple groups was completed.
Authored by one of the key contributors to these developments, a major theme of the book is the growing role that geometry has played in this story in the form of diagram geometries, amalgams, graph theory and “pushing up”. The chapters interweave various ideas and techniques applicable to all sporadic groups. Many of the results presented—several due to the author and collaborators—appear in book form for the first time. While much of the book describes developments from recent decades, it also includes significant new material, notably on the enigmatic Thompson group and the Monster. The final chapter explores connections to Majorana algebras and discusses some remarkable conjectures.
A valuable addition to the literature on finite simple groups, this book will appeal to a wide audience, from advanced graduate students to researchers in group theory, combinatorics, finite geometry, coding theory, graph theory, and other mathematical fields that use group theory to study symmetries and structures.
Table of Contents:
1 Basic Group Theory.- 2 Permutation Groups.- 3 Locally Symmetric Graphs.- 4 Dual Polar Spaces.- 5 The Dickson Group ----2(3).- 6 Graphs Which Are Locally Something.- 7 Petersen and Tilde Geometries.- 8 Locally Projective Graphs.- 9 Geometry of the Thompson Group.- 10 Pushing Up.- 11 Buekenhout–Fisher Geometry for the Monster.- 12 Moonshine and Majorana.
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