000 03671nam a22005655i 4500
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020 _a9783031623486
_9978-3-031-62348-6
024 7 _a10.1007/978-3-031-62348-6
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBG
_2thema
100 1 _aBubboloni, Daniela.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981056
245 1 0 _aNormal 2-Coverings of the Finite Simple Groups and their Generalizations
_h[electronic resource] /
_cby Daniela Bubboloni, Pablo Spiga, Thomas Stefan Weigel.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aX, 180 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 ;
_v2352
505 0 _a- Introduction -- Preliminaries -- Linear groups -- Unitary groups -- Symplectic groups -- Odd dimensional orthogonal groups -- Orthogonal groups with Witt defect 1 -- Orthogonal groups with Witt defect 0 -- Proofs of the main theorems -- Almost simple groups having socle a sporadic simple group -- Dropping the maximality -- Degenerate normal 2-coverings.
520 _aThis book provides a complete and comprehensive classification of normal 2-coverings of non-abelian simple groups and their generalizations. While offering readers a thorough understanding of these structures, and of the groups admitting them, it delves into the properties of weak normal coverings. The focal point is the weak normal covering number of a group G, the minimum number of proper subgroups required for every element of G to have a conjugate within one of these subgroups, via an element of Aut(G). This number is shown to be at least 2 for every non-abelian simple group and the non-abelian simple groups for which this minimum value is attained are classified. The discussion then moves to almost simple groups, with some insights into their weak normal covering numbers. Applications span algebraic number theory, combinatorics, Galois theory, and beyond. Compiling existing material and synthesizing it into a cohesive framework, the book gives a complete overview of this fundamental aspect of finite group theory. It will serve as a valuable resource for researchers and graduate students working on non-abelian simple groups,.
650 0 _aGroup theory.
_970149
650 0 _aDiscrete mathematics.
650 0 _aGraph theory.
650 1 4 _aGroup Theory and Generalizations.
_970154
650 2 4 _aApplications of Discrete Mathematics.
_967427
650 2 4 _aGraph Theory.
700 1 _aSpiga, Pablo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981057
700 1 _aWeigel, Thomas Stefan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981058
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031623479
776 0 8 _iPrinted edition:
_z9783031623493
830 0 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2352
_975434
856 4 0 _uhttps://doi.org/10.1007/978-3-031-62348-6
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
999 _c61818
_d61818