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Ever-Evolving Groups
An Introduction to Modern Finite Group Theory
Buch von Alexander A. Ivanov
Sprache: Englisch

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Beschreibung
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.
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2025
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xiv
339 S.
1 farbige Illustr.
339 p. 1 illus. in color.
ISBN-13: 9783031890109
ISBN-10: 3031890108
Sprache: Englisch
Einband: Gebunden
Autor: Ivanov, Alexander A.
Hersteller: Springer Nature Switzerland
Springer International Publishing
Springer International Publishing AG
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 24 mm
Von/Mit: Alexander A. Ivanov
Erscheinungsdatum: 01.06.2025
Gewicht: 0,762 kg
Artikel-ID: 133432754
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2025
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xiv
339 S.
1 farbige Illustr.
339 p. 1 illus. in color.
ISBN-13: 9783031890109
ISBN-10: 3031890108
Sprache: Englisch
Einband: Gebunden
Autor: Ivanov, Alexander A.
Hersteller: Springer Nature Switzerland
Springer International Publishing
Springer International Publishing AG
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 24 mm
Von/Mit: Alexander A. Ivanov
Erscheinungsdatum: 01.06.2025
Gewicht: 0,762 kg
Artikel-ID: 133432754
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