Character correspondences in finite groups [Elektronische Ressource] / vorgelegt von Frieder Ladisch

Frieder Ladisch

Description

Character Correspondencesin Finite GroupsDissertationzurErlangung des akademischen Gradesdoctor rerum naturalium (Dr. rer. nat.)der Mathematisch-Naturwissenschaftlichen Fakultat¨der Universit¨at Rostockvorgelegt vonFrieder Ladisch,geboren am 25. M¨arz 1977 in Karlsruhe,aus Rostockurn:nbn:de:gbv:28-diss2009-0106-4Rostock 2009Gutachter:Prof. Dr. Reinhard Knorr,¨ Universitat¨ RostockProf. Dr. Wolfgang Willems, Otto-von-Guericke-Universitat Magdeburg¨Tag der offentlichen Verteidigung:¨09. M¨arz 2009AbstractWe consider character correspondences between the characters of a grouplying over a fixed character of a normal subgroup, and a similar defined setof characters of a subgroup. This situation occurs in many applications,for example in the proof of important character correspondences found byGlauberman, Dade and Isaacs. With our methods we can give more trans-parent proofs of the results of Dade and Isaacs. We also consider ratio-nality questions and generalizations to modular representation theory. Weshow that the Isaacs part of the Glauberman-Isaacs correspondence preservesSchur indices.ContentsContents iIntroduction iii1 Central Simple Algebras 12 A Character Correspondence 62.1 Magic Representations ...................... 62.2 Semi-Invariant Characters .................... 19Clifford Theory with Fields ................... 20Magic Crossed Representations ................. 22Digression: Group Action on Simple Algebras ......... 282.

Sujets

• Mathematics

Informations

• Publié par: universitat_rostock
• Publié le: 01 janvier 2009
• Nombre de lectures: 36
• Langue: Deutsch
• Poids de l'ouvrage: 1 Mo

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