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020 _a9783031629150
_9978-3-031-62915-0
024 7 _a10.1007/978-3-031-62915-0
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBG
_2thema
100 1 _aKorhonen, Mikko.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981388
245 1 0 _aMaximal Solvable Subgroups of Finite Classical Groups
_h[electronic resource] /
_cby Mikko Korhonen.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aVIII, 298 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2346
505 0 _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.
520 _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.
650 0 _aGroup theory.
_970149
650 1 4 _aGroup Theory and Generalizations.
_970154
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031629143
776 0 8 _iPrinted edition:
_z9783031629167
830 0 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2346
_975434
856 4 0 _uhttps://doi.org/10.1007/978-3-031-62915-0
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
999 _c61966
_d61966