國立虎尾科技大學 |

Ever-evolving groups = an introduction to modern finite group theory /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Ever-evolving groups/ by Alexander A. Ivanov.
Reminder of title:	an introduction to modern finite group theory /
Author:	Ivanov, A. A.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xiv, 339 p. :ill. (chiefly color), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Finite groups. -
Online resource:	https://doi.org/10.1007/978-3-031-89011-6
ISBN:	9783031890116

Ever-evolving groups = an introduction to modern finite group theory /
Ivanov, A. A.

Ever-evolving groupsan introduction to modern finite group theory /[electronic resource] :by Alexander A. Ivanov. - Cham :Springer Nature Switzerland :2025. - xiv, 339 p. :ill. (chiefly color), digital ;24 cm. - Algebra and applications,v. 322192-2950 ;. - Algebra and applications ;v.17..

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.

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.

ISBN: 9783031890116

Standard No.: 10.1007/978-3-031-89011-6doiSubjects--Topical Terms:

684448
Finite groups.

LC Class. No.: QA174

Dewey Class. No.: 512.23

Ever-evolving groups = an introduction to modern finite group theory /
LDR:02725nam a2200337 a 4500 001 1162552
003 DE-He213
005 20250601130238.0
006 m d
007 cr nn 008maaau
008 251029s2025 sz s 0 eng d
020 $a 9783031890116 $q (electronic bk.)
020 $a 9783031890109 $q (paper)
024 7 $a 10.1007/978-3-031-89011-6 $2 doi
035 $a 978-3-031-89011-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA174
072 7 $a PBG $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBG $2 thema
082 0 4 $a 512.23 $2 23
090 $a QA174 $b .I93 2025
100 1 $a Ivanov, A. A. $3 1489355
245 1 0 $a Ever-evolving groups $h [electronic resource] : $b an introduction to modern finite group theory / $c by Alexander A. Ivanov.
260 $a Cham : $c 2025. $b Springer Nature Switzerland : $b Imprint: Springer,
300 $a xiv, 339 p. : $b ill. (chiefly color), digital ; $c 24 cm.
490 1 $a Algebra and applications, $x 2192-2950 ; $v v. 32
505 0 $a 1 Basic Group Theory -- 2 Permutation Groups -- 3 Locally Symmetric Graphs -- 4 Dual Polar Spaces -- 5 The Dickson Group 𝑮2(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.
520 $a 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.
650 0 $a Finite groups. $3 684448
650 1 4 $a Group Theory and Generalizations. $3 672112
650 2 4 $a Graph Theory. $3 786670
650 2 4 $a Convex and Discrete Geometry. $3 672138
650 2 4 $a Projective Geometry. $3 1021390
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Algebra and applications ; $v v.17. $3 888960
856 4 0 $u https://doi.org/10.1007/978-3-031-89011-6
950 $a Mathematics and Statistics (SpringerNature-11649)