LEADER 03550nam 22005535 450 001 9910878063703321 005 20260112092133.0 010 $a9783031629150$b(electronic bk.) 010 $z9783031629143 024 7 $a10.1007/978-3-031-62915-0 035 $a(MiAaPQ)EBC31569884 035 $a(Au-PeEL)EBL31569884 035 $a(CKB)33469061100041 035 $a(DE-He213)978-3-031-62915-0 035 $a(PPN)279810008 035 $a(EXLCZ)9933469061100041 100 $a20240727d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMaximal Solvable Subgroups of Finite Classical Groups /$fby Mikko Korhonen 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (viii, 298 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2346 311 08$aPrint version: Korhonen, Mikko Maximal Solvable Subgroups of Finite Classical Groups Cham : Springer,c2024 9783031629143 320 $aIncludes bibliographical references and index. 327 $a- Introduction -- Basic structure of maximal irreducible solvable subgroups -- Extraspecial groups -- Metrically primitive maximal irreducible solvable subgroups -- Basic properties of GB ?,?(X1, . . . ,Xk) -- Fixed point spaces and abelian subgroups -- Maximality of the groups constructed -- Examples. 330 $aThis book studies maximal solvable subgroups of classical groups over finite fields. It provides the first modern account of Camille Jordan's classical results, and extends them, giving a classification of maximal irreducible solvable subgroups of general linear groups, symplectic groups, and orthogonal groups over arbitrary finite fields. A subgroup of a group G is said to be maximal solvable if it is maximal among the solvable subgroups of G. The history of this notion goes back to Jordan?s Traité (1870), in which he provided a classification of maximal solvable subgroups of symmetric groups. The main difficulty is in the primitive case, which leads to the problem of classifying maximal irreducible solvable subgroups of general linear groups over a field of prime order. One purpose of this monograph is expository: to give a proof of Jordan?s classification in modern terms. More generally, the aim is to generalize these results to classical groups over arbitrary finite fields, and to provide other results of interest related to irreducible solvable matrix groups. The text will be accessible to graduate students and researchers interested in primitive permutation groups, irreducible matrix groups, and related topics in group theory and representation theory. The detailed introduction will appeal to those interested in the historical background of Jordan?s work. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2346 606 $aGroup theory 606 $aGroup Theory and Generalizations 606 $aTeoria de grups$2thub 606 $aGrups finits$2thub 608 $aLlibres electrònics$2thub 615 0$aGroup theory. 615 14$aGroup Theory and Generalizations. 615 7$aTeoria de grups. 615 7$aGrups finits 676 $a512.2 700 $aKorhonen$b Mikko$g(Mikko Tapani),$0741929 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910878063703321 996 $aMaximal Solvable Subgroups of Finite Classical Groups$94196806 997 $aUNINA