Axioms (Oct 2023)

Irreducible Characters with Cyclic Anchor Group

  • Manal H. Algreagri,
  • Ahmad M. Alghamdi

DOI
https://doi.org/10.3390/axioms12100950
Journal volume & issue
Vol. 12, no. 10
p. 950

Abstract

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We consider G to be a finite group and p as a prime number. We fix ψ to be an irreducible character of G with its restriction to all p-regular elements of G and ψ0 to be an irreducible Brauer character. The main aim of this paper is to describe and investigate the relationship between cyclic anchor group of ψ and the defect group of a p-block which contains ψ. Our methods are to study and generalize some facts for the cyclic defect groups of a p-block B to the case of a cyclic anchor group of irreducible characters which belong to B. We establish and prove a criteria for an irreducible character to have a cyclic anchor group.

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