Quasi-isolated blocks and the Malle-Robinson conjecture

In a recent paper, G. Malle and G. Robinson proposed a modular anologue to Brauer's famous \( k(B) \)-conjecture. If \( B \) is a \( p \)-block of a finite group with defect group \( D \), then they conjecture that \( l(B) \leq p^r \), where \( r \) is the sectional \( p \)-rank of \( D \). Since this conjecture is relatively new, there is obviously still a lot of work to do. This thesis is concerned with proving their conjecture for the finite groups of exceptional Lie type.

Metadaten
Author:	Ruwen Hollenbach
URN:	urn:nbn:de:hbz:386-kluedo-59430
Advisor:	Gunter Malle
Document Type:	Doctoral Thesis
Language of publication:	English
Date of Publication (online):	2020/04/01
Year of first Publication:	2020
Publishing Institution:	Technische Universität Kaiserslautern
Granting Institution:	Technische Universität Kaiserslautern
Acceptance Date of the Thesis:	2019/04/11
Date of the Publication (Server):	2020/04/02
Page Number:	V, 80
Faculties / Organisational entities:	Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:	5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):	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
Licence (German):	Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)