Cartan matrices and Brauer's k(B)-Conjecture V

Cesare G. Ardito; Benjamin Sambale

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arXiv · 1911.10710

Cartan matrices and Brauer's k(B)-Conjecture V

Cesare G. Ardito·Benjamin Sambale

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Abstract

We prove Brauer's k(B)-Conjecture for the 3-blocks with abelian defect groups of rank at most 5 and for all 3-blocks of defect at most 4. For this purpose we develop a computer algorithm to construct isotypies based on a method of Usami and Puig. This leads further to some previously unknown perfect isometries for the 5-blocks of defect 2. We also investigate basic sets which are compatible under the action of the inertial group.

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Cesare G. Ardito, Benjamin Sambale. 2019-11-25. Cartan matrices and Brauer's k(B)-Conjecture V. https://arxiv.org/abs/1911.10710

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