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Finite non-solvable groups with few 2-parts of co-degrees of irreducible characters | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 10، دوره 4، شماره 1، 2023، صفحه 87-89 اصل مقاله (305.2 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21894.1119 | ||
| نویسنده | ||
| Neda Ahanjideh* | ||
| Department of pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran | ||
| چکیده | ||
| For a character $ \chi $ of a finite group $ G $, the number $ \chi^c(1)=\frac{[G:{\rm ker}\chi]}{\chi(1)} $ is called the co-degree of $ \chi $. Let ${\rm Sol}(G)$ denote the solvable radical of $G$. In this paper, we show that if $G$ is a finite non-solvable group with $\{\chi^c(1)_2:\chi \in {\rm Irr}(G)\}=\{1,2^m\}$ for some positive integer $m$, then $G/{\rm Sol}(G)$ has a normal subgroup $M/{\rm Sol}(G)$ such that $M/{\rm Sol}(G)\cong {\rm PSL}_2(2^n)$ for some integer $n \geq 2$, $[G:M]$ is odd and $ G/{\rm Sol}(G) \lesssim {\rm Aut}({\rm PSL}_2(2^n))$. | ||
| کلیدواژه‌ها | ||
| The co-degree of a character؛ Non-solvable groups؛ Irreducible character degrees | ||
| مراجع | ||
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[1] N. Ahanjideh, On the p-solvable groups with few p-parts of irreducible character co-degrees. Submitted.
[2] , The Fitting subgroup, p-length, derived length and character table, Mathematische Nachrichten, 294 (2021), pp. 214–223.
[3] , The one-prime hypothesis on the co-degrees of irreducible characters, Communications in Algebra, 49 (2021), pp. 4016–4020.
[4] , Co-degree graphs and order elements, Bulletin of the Malaysian Mathematical Sciences Society, 45 (2022), pp. 2653–2664.
[5] , Finite groups admitting at most two irreducible characters having equal co-degrees, Journal of Algebra and Its Applications, (2022), p. 2350098.
[6] , Nondivisibility among irreducible character co-degrees, Bulletin of the Australian Mathematical Society, 105 (2022), pp. 68–74.
[7] Z. Akhlaghi, M. Ebrahimi, and M. Khatami, On the multiplicities of the character codegrees of finite groups, Algebras and Representation Theory, (2022), pp. 1–16. [8] R. Bahramian and N. Ahanjideh, p-divisibility of co-degrees of irreducible characters, Bull. Aust. Math. Soc., 103 (2021), pp. 78–82. [9] , p-parts of co-degrees of irreducible characters, Comptes Rendus. Math´ematique, 359 (2021), pp. 79–83. [10] R. Bahramian, N. Ahanjideh, and A. R. Naghipour, Groups with some cube-free irreducible character co-degrees, Communications in Algebra, (2022), pp. 1–5.
[11] N. N. Hung, Characters of p 0 -degree and Thompson’s character degree theorem, Revista matem´atica iberoamer[1]icana, 33 (2017), pp. 117–138.
[12] I. M. Isaacs, Character theory of finite groups, Dover Publications, Inc., New York, 1994. Corrected reprint of the 1976 original [Academic Press, New York].
[13] Y. Liu, Nonsolvable groups whose irreducible character degrees have special 2-parts, Frontiers of Mathematics in China, (2021), pp. 1–6.
[14] A. Moreto´, A dual version of Huppert’s ρ-σ conjecture for character codegrees, Forum Math., 34 (2022), pp. 425–430.
[15] A. Moreto and N. Rizo ´ , Kernels of p 0 -degree irreducible characters, Mediterr. J. Math., 19 (2022), pp. Paper No. 121, 8.
[16] G. Navarro and P. H. Tiep, Degrees of rational characters of finite groups, Adv. Math., 224 (2010), pp. 1121–1142.
[17] G. Qian, Y. Wang, and H. Wei, Co-degrees of irreducible characters in finite groups, J. Algebra, 312 (2007), pp. 946–955.
[18] Y. Yang and G. Qian, The analog of Huppert’s conjecture on character codegrees, J. Algebra, 478 (2017), pp. 215–219. | ||
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