03267nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001500165072002300180072001400203100007600217245014300293250001800436264006900454300004200523336002600565337002600591338003600617347002400653490006300677505038000740520098801120650001702108650001302125650002202138650001802160650003402178650001702212650001302229650002002242650003802262650003302300650005402333700007302387710003402460773002602494776003602520776003602556776003602592830006302628856004602691978-3-031-50706-9DE-He21320251030111815.0cr nn 008mamaa240412s2024    sz |    s    |||| 0|eng d  a97830315070697 a10.1007/978-3-031-50706-92doi 4aQA1-939 7aPB2bicssc 7aMAT0000002bisacsh 7aPB2thema1 aCossey, James.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aCharacters and Blocks of Solvable Groupsh[electronic resource] :bA User’s Guide to Large Orbit Theorems /cby James Cossey, Yong Yang.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aIX, 159 p. 1 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSynthesis Lectures on Mathematics & Statistics,x1938-17510 aIntroduction -- Background Material -- Solvable Linear Groups and Gluck’s Permutation Lemma -- Gluck’s Conjecture -- The Huppert ρ-σ Conjecture -- Dolfi’s Theorem -- Induction and Restriction of Characters From p-Complements -- Brauer Graphs of Solvable Groups, I -- Brauer Graphs of Solvable Groups, II -- Conjugacy Classes, Codegrees, Zeros, and other Applications.  aThis book highlights recent developments in the representation theory of finite solvable groups, which seeks to connect group theory to linear algebra in ways that allow for better study of the groups in question. Over the last several decades, a number of results in the representations of solvable groups have been proven using so-called “large orbit” theorems. This book provides an extensive survey of the current state of the large-orbit theorems. The authors outline the proofs of the large orbit theorems to provide an overview of the topic, then demonstrate how these theorems can be used to prove new results about solvable groups. In addition, this book: Discusses recent developments in the representation theory of finite solvable groups Provides an extensive survey of the current state of the large-orbit theorems, providing a broad overview of the topic Includes proofs that demonstrate how these theorems can be applied to prove new results about solvable groups. 0aMathematics. 0aAlgebra. 0aAlgebras, Linear. 0aGroup theory. 0aMathematicsxData processing.14aMathematics.24aAlgebra.24aLinear Algebra.24aGroup Theory and Generalizations.24aApplications of Mathematics.24aComputational Mathematics and Numerical Analysis.1 aYang, Yong.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303150705208iPrinted edition:z978303150707608iPrinted edition:z9783031507083 0aSynthesis Lectures on Mathematics & Statistics,x1938-175140uhttps://doi.org/10.1007/978-3-031-50706-9