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2013 Further evidence for conjectures in block theory
Benjamin Sambale
Algebra Number Theory 7(9): 2241-2273 (2013). DOI: 10.2140/ant.2013.7.2241


We prove new inequalities concerning Brauer’s k(B)-conjecture and Olsson’s conjecture by generalizing old results. After that, we obtain the invariants for 2-blocks of finite groups with certain bicyclic defect groups. Here, a bicyclic group is a product of two cyclic subgroups. This provides an application for the classification of the corresponding fusion systems in a previous paper. To some extent, this generalizes previously known cases with defect groups of types D2n×C2m, Q2n×C2m and D2nC2m. As a consequence, we prove Alperin’s weight conjecture and other conjectures for several new infinite families of nonnilpotent blocks. We also prove Brauer’s k(B)-conjecture and Olsson’s conjecture for the 2-blocks of defect at most 5. This completes results from a previous paper. The k(B)-conjecture is also verified for defect groups with a cyclic subgroup of index at most 4. Finally, we consider Olsson’s conjecture for certain 3-blocks.


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Benjamin Sambale. "Further evidence for conjectures in block theory." Algebra Number Theory 7 (9) 2241 - 2273, 2013.


Received: 30 September 2012; Revised: 16 October 2012; Accepted: 23 March 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1290.20010
MathSciNet: MR3152013
Digital Object Identifier: 10.2140/ant.2013.7.2241

Primary: 20C15
Secondary: 20C20

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.7 • No. 9 • 2013
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