$p$-parts of co-degrees of irreducible characters

Roya Bahramian; Neda Ahanjideh

doi:10.5802/crmath.158

Théorie des groupes

p

-parts of co-degrees of irreducible characters

Roya Bahramian ¹ ; Neda Ahanjideh ¹

¹ Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran

Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 79-83

Résumé

For a character $χ$ of a finite group $G$ , the co-degree of $χ$ is $χ^{c} (1) = \frac{[G : ker χ]}{χ (1)}$ . Let $p$ be a prime and let $e$ be a positive integer. In this paper, we first show that if $G$ is a $p$ -solvable group such that $p^{e + 1} ∤ χ^{c} (1)$ , for every irreducible character $χ$ of $G$ , then the $p$ -length of $G$ is not greater than $e$ . Next, we study the finite groups satisfying the condition that $p^{2}$ does not divide the co-degrees of their irreducible characters.

Reçu le : 2020-04-22
Révisé le : 2020-11-24
Accepté le : 2020-11-24
Publié le : 2021-03-01

Zbl

DOI : 10.5802/crmath.158

Classification : 20C15, 20D10, 20D05

Affiliations des auteurs :

Roya Bahramian ¹ ; Neda Ahanjideh ¹

¹ Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {$p$-parts of co-degrees of irreducible characters},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {79--83},
     year = {2021},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {1},
     doi = {10.5802/crmath.158},
     zbl = {07302537},
     language = {en},
}

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Roya Bahramian; Neda Ahanjideh. $p$-parts of co-degrees of irreducible characters. Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 79-83. doi: 10.5802/crmath.158

Bibliographie
Cité par

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