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

Cesare Giulio Ardito, Benjamin Sambale

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)670-699
Number of pages30
JournalJournal of Algebra
Early online date31 May 2022
Publication statusPublished - 15 Sept 2022


  • Brauer's conjecture
  • Number of characters
  • Perfect isometries
  • Usami–Puig method


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