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

For a character χ of a finite group G, the co-degree of χ is χ c (1)=[G:kerχ] 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.

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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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     title = {$p$-parts of co-degrees of irreducible characters},
     journal = {Comptes Rendus. Math\'ematique},
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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/

[1] Neda Ahanjideh The Fitting subgroup, p-length, derived length and character table (2020) (to appear in Math. Nachr., https://www.doi.org/10.1002/mana.202000057)

[2] Roya Bahramian; Neda Ahanjideh p-divisibility of co-degrees of irreducible characters (2020) (to appear in Bull. Aust. Math. Soc., https://www.doi.org/10.1017/S0004972720000295) | Article

[3] Ni Du; Mark L. Lewis Codegrees and nilpotence class of p-groups, J. Group Theory, Volume 19 (2016) no. 4, pp. 561-568 | MR 3518392 | Zbl 1350.20006

[4] Eugenio Giannelli; Noelia Rizo; A. A. Schaeffer Fry Groups with few p -character degrees, J. Pure Appl. Algebra, Volume 224 (2020) no. 8, 106338, 15 pages | MR 4074578 | Zbl 07187749

[5] Bertram Huppert Endliche Gruppen I, Grundlehren der Mathematischen Wissenschaften, 134, Springer, 1967 | MR 224703 | Zbl 0217.07201

[6] I. Martin Isaacs Character theory of finite groups, Dover Publications, 1994 | MR 1280461 | Zbl 0849.20004

[7] Peter Kleidman; Martin Liebeck The subgroup structure of the finite classical groups, London Mathematical Society Lecture Note Series, 129, London Mathematical Society, 1990 | MR 1057341 | Zbl 0697.20004

[8] Mark L. Lewis; Gabriel Navarro; Pham Huu Tiep; Hung P. Tong-Viet p-parts of character degrees, J. Lond. Math. Soc., Volume 92 (2015) no. 2, pp. 483-497 | Article | MR 3404035 | Zbl 1335.20006

[9] Mark L. Lewis; Gabriel Navarro; Thomas R. Wolf p-parts of character degrees and the index of the Fitting subgroup, J. Algebra, Volume 411 (2014), pp. 182-190 | Article | MR 3210924 | Zbl 1305.20007

[10] Guohua Qian A note on p-parts of character degrees, Bull. Lond. Math. Soc., Volume 50 (2018) no. 4, pp. 663-666 | Article | MR 3870949 | Zbl 06930196

[11] Guohua Qian; Yanming Wang; Huaquan Wei Co-degrees of irreducible characters in finite groups, J. Algebra, Volume 312 (2007) no. 2, pp. 946-955 | Article | MR 2333193 | Zbl 1127.20009

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