03456nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202072001500225100008800240245016000328250001800488264006900506300003200575336002600607337002600633338003600659347002400695490005300719505036200772520115201134650002502286650002602311650001802337650004502355650004902400650001802449700008202467700009102549710003402640773002602674776003602700776003602736830006002772856004602832912001402878912001502892912001402907999001702921978-3-031-62348-6DE-He21320251030112643.0cr nn 008mamaa240723s2024    sz |    s    |||| 0|eng d  a97830316234869978-3-031-62348-67 a10.1007/978-3-031-62348-62doi 4aQA174-183 7aPBG2bicssc 7aMAT0020102bisacsh 7aPBG2thema1 aBubboloni, Daniela.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98105610aNormal 2-Coverings of the Finite Simple Groups and their Generalizationsh[electronic resource] /cby Daniela Bubboloni, Pablo Spiga, Thomas Stefan Weigel.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aX, 180 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Mathematics,x1617-9692 ;v23520 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.  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,. 0aGroup theory.970149 0aDiscrete mathematics. 0aGraph theory.14aGroup Theory and Generalizations.97015424aApplications of Discrete Mathematics.96742724aGraph Theory.1 aSpiga, Pablo.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9810571 aWeigel, Thomas Stefan.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9810582 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303162347908iPrinted edition:z9783031623493 0aLecture Notes in Mathematics,x1617-9692 ;v235297543440uhttps://doi.org/10.1007/978-3-031-62348-6  aZDB-2-SMA  aZDB-2-SXMS  aZDB-2-LNM  c61818d61818