LEADER 04035nam 22007935 450 001 9911007484803321 005 20260209162125.0 010 $a3-031-89011-6 024 7 $a10.1007/978-3-031-89011-6 035 $a(MiAaPQ)EBC32144050 035 $a(Au-PeEL)EBL32144050 035 $a(CKB)39151533500041 035 $a(DE-He213)978-3-031-89011-6 035 $a(EXLCZ)9939151533500041 100 $a20250601d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEver-Evolving Groups $eAn Introduction to Modern Finite Group Theory /$fby Alexander A. Ivanov 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (346 pages) 225 1 $aAlgebra and Applications,$x2192-2950 ;$v32 311 08$a3-031-89010-8 327 $a1 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. 330 $aThis book presents an original approach to the theory of finite groups, placing finite sporadic groups on an equal footing. It provides a nearly comprehensive overview of developments in the study of sporadic groups since the classification of finite simple groups was completed. Authored by one of the key contributors to these developments, a major theme of the book is the growing role that geometry has played in this story in the form of diagram geometries, amalgams, graph theory and ?pushing up?. The chapters interweave various ideas and techniques applicable to all sporadic groups. Many of the results presented?several due to the author and collaborators?appear in book form for the first time. While much of the book describes developments from recent decades, it also includes significant new material, notably on the enigmatic Thompson group and the Monster. The final chapter explores connections to Majorana algebras and discusses some remarkable conjectures. A valuable addition to the literature on finite simple groups, this book will appeal to a wide audience, from advanced graduate students to researchers in group theory, combinatorics, finite geometry, coding theory, graph theory, and other mathematical fields that use group theory to study symmetries and structures. 410 0$aAlgebra and Applications,$x2192-2950 ;$v32 606 $aGroup theory 606 $aGraph theory 606 $aConvex geometry 606 $aDiscrete geometry 606 $aGeometry, Projective 606 $aGroup Theory and Generalizations 606 $aGraph Theory 606 $aConvex and Discrete Geometry 606 $aProjective Geometry 606 $aGeometria projectiva$2thub 606 $aGeometria convexa$2thub 606 $aGeometria discreta$2thub 606 $aTeoria de grafs$2thub 606 $aTeoria de grups$2thub 606 $aÀlgebra$2thub 608 $aLlibres electrònics$2thub 615 0$aGroup theory. 615 0$aGraph theory. 615 0$aConvex geometry. 615 0$aDiscrete geometry. 615 0$aGeometry, Projective. 615 14$aGroup Theory and Generalizations. 615 24$aGraph Theory. 615 24$aConvex and Discrete Geometry. 615 24$aProjective Geometry. 615 7$aGeometria projectiva 615 7$aGeometria convexa 615 7$aGeometria discreta 615 7$aTeoria de grafs 615 7$aTeoria de grups 615 7$aÀlgebra 676 $a512.2 700 $aIvanov$b Alexander A$0422816 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911007484803321 996 $aEver-Evolving Groups$94387813 997 $aUNINA