Group theory
Rational Groups whose character degree graphs are disconnected
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 711-715.

A finite group all of whose complex character values are rational is called a rational group. In this paper, we classify all rational groups whose character degree graphs are disconnected.

Un groupe fini dont toutes les valeurs de caractères complexes sont rationnelles est appelé un groupe rationnel. Dans cet article, nous classifions tous les groupes rationnels dont les graphes de degrés de caractère sont déconnectés.

Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.337
Classification: 20C15
Temha Erkoç 1; Gamze Akar 2

1 Istanbul University, Faculty of Science, Department of Mathematics, 34134 Istanbul,Turkey
2 Istinye University, Faculty of Engineering and Natural Sciences, Department of Mathematics, 34396 Istanbul,Turkey
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Temha Erkoç; Gamze Akar. Rational Groups whose character degree graphs are disconnected. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 711-715. doi : 10.5802/crmath.337. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.337/

[1] Michael J. J. Barry; Michael B. Ward On a conjecture of Alvis, J. Algebra, Volume 294 (2005) no. 1, pp. 136-155 | DOI | MR | Zbl

[2] John H. Conway; Robert T. Curtis; Simon P. Norton; Richard A. Parker; Robert A. Wilson Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups, with Computational Assistance from J.G. Thackray, Clarendon Press, 1985

[3] Walter Feit; Gary M. Seitz On finite rational groups and related topics, Ill. J. Math., Volume 33 (1989) no. 1, pp. 103-131 | MR | Zbl

[4] Roderick Gow Groups whose characters are rational-valued, J. Algebra, Volume 40 (1976) no. 1, pp. 280-299 | MR | Zbl

[5] Pál Hegedűs Structure of solvable rational groups, Proc. Lond. Math. Soc., Volume 90 (2005) no. 2, pp. 439-471 | MR | Zbl

[6] Bertram Huppert Endliche Gruppen I, Grundlehren der Mathematischen Wissenschaften, 134, Springer, 1967 | DOI

[7] I. Martin Isaacs Character Theory of Finite Groups, Pure and Applied Mathematics, 69, Academic Press Inc., 1976 | MR

[8] Dennis Kletzing Structure and Representations of Q-Groups, Lecture Notes in Mathematics, 1084, Springer, 1984 | DOI | MR

[9] Mark L. Lewis Solvable groups whose degree graphs have two connected components, J. Group Theory, Volume 4 (2001) no. 3, pp. 255-275 | MR | Zbl

[10] Mark L. Lewis; Donald L. White Connectedness of degree graphs of nonsolvable groups, J. Algebra, Volume 266 (2003) no. 1, pp. 51-76 | DOI | MR | Zbl

[11] Olaf Manz; Wolfgang Willems; Thomas R. Wolf The diameter of the character degree graph, J. Reine Angew. Math., Volume 402 (1989), pp. 181-198 | MR | Zbl

[12] Péter Pál Pálfy On the character degree graph of solvable groups. I: Three primes, Period. Math. Hung., Volume 36 (1998) no. 1, pp. 61-65 | DOI | MR | Zbl

[13] Farideh Shafiei; Mohammad Reza Darafsheh; Farrokh Shirjian Rational Nearly Simple Groups, Bull. Aust. Math. Soc., Volume 103 (2021) no. 3, pp. 475-485 | DOI | MR | Zbl

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