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The Inductive Blockwise Alperin Weight Condition for the Finite Groups \( SL_3(q) \) \( (3 \nmid (q-1)) \), \( G_2(q) \) and \( ^3D_4(q) \)

  • The central topic of this thesis is Alperin's weight conjecture, a problem concerning the representation theory of finite groups. This conjecture, which was first proposed by J. L. Alperin in 1986, asserts that for any finite group the number of its irreducible Brauer characters coincides with the number of conjugacy classes of its weights. The blockwise version of Alperin's conjecture partitions this problem into a question concerning the number of irreducible Brauer characters and weights belonging to the blocks of finite groups. A proof for this conjecture has not (yet) been found. However, the problem has been reduced to a question on non-abelian finite (quasi-) simple groups in the sense that there is a set of conditions, the so-called inductive blockwise Alperin weight condition, whose verification for all non-abelian finite simple groups implies the blockwise Alperin weight conjecture. Now the objective is to prove this condition for all non-abelian finite simple groups, all of which are known via the classification of finite simple groups. In this thesis we establish the inductive blockwise Alperin weight condition for three infinite series of finite groups of Lie type: the special linear groups \(SL_3(q)\) in the case \(q>2\) and \(q \not\equiv 1 \bmod 3\), the Chevalley groups \(G_2(q)\) for \(q \geqslant 5\), and Steinberg's triality groups \(^3D_4(q)\).

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Metadaten
Verfasserangaben:Elisabeth Schulte
URN (Permalink):urn:nbn:de:hbz:386-kluedo-42250
Betreuer:Gunter Malle
Dokumentart:Dissertation
Sprache der Veröffentlichung:Englisch
Veröffentlichungsdatum (online):06.11.2015
Jahr der Veröffentlichung:2015
Veröffentlichende Institution:Technische Universität Kaiserslautern
Titel verleihende Institution:Technische Universität Kaiserslautern
Datum der Annahme der Abschlussarbeit:16.10.2015
Datum der Publikation (Server):09.11.2015
Seitenzahl:IX, 226
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Klassifikation (Mathematik):20-XX GROUP THEORY AND GENERALIZATIONS / 20Cxx Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)] / 20C15 Ordinary representations and characters
20-XX GROUP THEORY AND GENERALIZATIONS / 20Cxx Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)] / 20C20 Modular representations and characters
20-XX GROUP THEORY AND GENERALIZATIONS / 20Cxx Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)] / 20C33 Representations of finite groups of Lie type
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vom 30.07.2015