03080nam a22003975i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072002300183072001500206100007800221245010300299250001800402264006900420300003500489336002600524337002600550338003600576347002400612490005300636505031000689520139600999650001802395650003802413710003402451773002602485776003602511776003602547830005302583856004602636978-3-031-62915-0DE-He21320251030112653.0cr nn 008mamaa240727s2024    sz |    s    |||| 0|eng d  a97830316291507 a10.1007/978-3-031-62915-02doi 4aQA174-183 7aPBG2bicssc 7aMAT0020102bisacsh 7aPBG2thema1 aKorhonen, Mikko.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aMaximal Solvable Subgroups of Finite Classical Groupsh[electronic resource] /cby Mikko Korhonen.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aVIII, 298 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Mathematics,x1617-9692 ;v23460 a- Introduction -- Basic structure of maximal irreducible solvable subgroups -- Extraspecial groups -- Metrically primitive maximal irreducible solvable subgroups -- Basic properties of GB μ,ν(X1, . . . ,Xk) -- Fixed point spaces and abelian subgroups -- Maximality of the groups constructed -- Examples.  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. 0aGroup theory.14aGroup Theory and Generalizations.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303162914308iPrinted edition:z9783031629167 0aLecture Notes in Mathematics,x1617-9692 ;v234640uhttps://doi.org/10.1007/978-3-031-62915-0