The blocks with five irreducible characters

J. Miquel Martínez; Noelia Rizo; Lucia Sanus

The blocks with five irreducible characters

Group Theory 2023-06-08 v1 Representation Theory

Authors: J. Miquel Martínez , Noelia Rizo , Lucia Sanus

Abstract

Let $G$ be a finite group, $p$ a prime and $B$ a Brauer $p$ -block of $G$ with defect group $D$ . We prove that if the number of irreducible ordinary characters in $B$ is $5$ then $D\cong C_5, C_7, D_8$ or $Q_8$ , assuming that the Alperin--McKay conjecture holds for $B$ .

Keywords

character theory character theory of finite groups

Cite

@article{arxiv.2306.04267,
  title  = {The blocks with five irreducible characters},
  author = {J. Miquel Martínez and Noelia Rizo and Lucia Sanus},
  journal= {arXiv preprint arXiv:2306.04267},
  year   = {2023}
}

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