Group theory
$p$-parts of co-degrees of irreducible characters
Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 79-83.

For a character $\chi$ of a finite group $G$, the co-degree of $\chi$ is ${\chi }^{c}\left(1\right)=\frac{\left[G:ker\chi \right]}{\chi \left(1\right)}$. 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 ${p}^{e+1}\nmid {\chi }^{c}\left(1\right)$, for every irreducible character $\chi$ 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.

Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/crmath.158
Classification: 20C15,  20D10,  20D05
Roya Bahramian 1; Neda Ahanjideh 1

1. Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.158/

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