04035nam 22007935 450 991100748480332120260209162125.03-031-89011-610.1007/978-3-031-89011-6(MiAaPQ)EBC32144050(Au-PeEL)EBL32144050(CKB)39151533500041(DE-He213)978-3-031-89011-6(EXLCZ)993915153350004120250601d2025 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierEver-Evolving Groups An Introduction to Modern Finite Group Theory /by Alexander A. Ivanov1st ed. 2025.Cham :Springer Nature Switzerland :Imprint: Springer,2025.1 online resource (346 pages)Algebra and Applications,2192-2950 ;323-031-89010-8 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.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.Algebra and Applications,2192-2950 ;32Group theoryGraph theoryConvex geometryDiscrete geometryGeometry, ProjectiveGroup Theory and GeneralizationsGraph TheoryConvex and Discrete GeometryProjective GeometryGeometria projectivathubGeometria convexathubGeometria discretathubTeoria de grafsthubTeoria de grupsthubÀlgebrathubLlibres electrònicsthubGroup theory.Graph theory.Convex geometry.Discrete geometry.Geometry, Projective.Group Theory and Generalizations.Graph Theory.Convex and Discrete Geometry.Projective Geometry.Geometria projectivaGeometria convexaGeometria discretaTeoria de grafsTeoria de grupsÀlgebra512.2Ivanov Alexander A422816MiAaPQMiAaPQMiAaPQBOOK9911007484803321Ever-Evolving Groups4387813UNINA