For a character of a finite group , the co-degree of is . Let be a prime and let be a positive integer. In this paper, we first show that if is a -solvable group such that , for every irreducible character of , then the -length of is not greater than . Next, we study the finite groups satisfying the condition that does not divide the co-degrees of their irreducible characters.
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.158
Roya Bahramian 1 ; Neda Ahanjideh 1
@article{CRMATH_2021__359_1_79_0, author = {Roya Bahramian and Neda Ahanjideh}, title = {$p$-parts of co-degrees of irreducible characters}, journal = {Comptes Rendus. Math\'ematique}, pages = {79--83}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {1}, year = {2021}, doi = {10.5802/crmath.158}, zbl = {07302537}, language = {en}, }
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] The Fitting subgroup, -length, derived length and character table (2020) (to appear in Math. Nachr., https://www.doi.org/10.1002/mana.202000057)
[2] -divisibility of co-degrees of irreducible characters (2020) (to appear in Bull. Aust. Math. Soc., https://www.doi.org/10.1017/S0004972720000295) | DOI | Zbl
[3] Codegrees and nilpotence class of -groups, J. Group Theory, Volume 19 (2016) no. 4, pp. 561-568 | MR | Zbl
[4] Groups with few -character degrees, J. Pure Appl. Algebra, Volume 224 (2020) no. 8, 106338, 15 pages | MR | Zbl
[5] Endliche Gruppen I, Grundlehren der Mathematischen Wissenschaften, 134, Springer, 1967 | MR | Zbl
[6] Character theory of finite groups, Dover Publications, 1994 | MR | Zbl
[7] The subgroup structure of the finite classical groups, London Mathematical Society Lecture Note Series, 129, London Mathematical Society, 1990 | MR | Zbl
[8] -parts of character degrees, J. Lond. Math. Soc., Volume 92 (2015) no. 2, pp. 483-497 | DOI | MR | Zbl
[9] -parts of character degrees and the index of the Fitting subgroup, J. Algebra, Volume 411 (2014), pp. 182-190 | DOI | MR | Zbl
[10] A note on -parts of character degrees, Bull. Lond. Math. Soc., Volume 50 (2018) no. 4, pp. 663-666 | DOI | MR | Zbl
[11] Co-degrees of irreducible characters in finite groups, J. Algebra, Volume 312 (2007) no. 2, pp. 946-955 | DOI | MR | Zbl
Cité par Sources :
Commentaires - Politique