Metabelian $ {\mathbb{Q}}_{1}$-groups

Mozhgan Rezakhanlou; Mohammad Reza Darafsheh

doi:10.1016/j.crma.2017.10.017

Algebra/Group theory

Metabelian

Q_{1}

-groups

Presented by: the Editorial Board

Mozhgan Rezakhanlou ¹; Mohammad Reza Darafsheh ²

¹ Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-137, Tehran, Iran
² School of Mathematics, Statistics, and Computer Science, College of Science, University of Tehran, Tehran, Iran

Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 138-140.

Abstract
Résumé

A finite group G is called a $Q_{1}$ -group if all of its non-linear irreducible characters are rational valued. In this paper, we will find the general structure of a metabelian $Q_{1}$ -group.

Un groupe fini G est appelé un $Q_{1}$ -groupe si les valeurs des caractères non linéaires sont rationnelles. Dans cet article, nous déterminons la structure des $Q_{1}$ -groupes métabéliens.

Received: 2017-03-09
Accepted: 2017-10-27
Published online: 2018-01-12

DOI: 10.1016/j.crma.2017.10.017

Author's affiliations:

Mozhgan Rezakhanlou ¹; Mohammad Reza Darafsheh ²

¹ Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-137, Tehran, Iran
² School of Mathematics, Statistics, and Computer Science, College of Science, University of Tehran, Tehran, Iran

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     author = {Mozhgan Rezakhanlou and Mohammad Reza Darafsheh},
     title = {Metabelian $ {\mathbb{Q}}_{1}$-groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {138--140},
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     number = {2},
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     doi = {10.1016/j.crma.2017.10.017},
     language = {en},
}

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Mozhgan Rezakhanlou; Mohammad Reza Darafsheh. Metabelian $ {\mathbb{Q}}_{1}$-groups. Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 138-140. doi : 10.1016/j.crma.2017.10.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.10.017/

References
Cited by

[1] B.G. Basmaji Rational non-linear characters of metabelian groups, Proc. Amer. Math. Soc., Volume 85 (1982) no. 2, pp. 175-180

[2] Y.A.G. Berkovich; E.M. Zhmud Characters of Finite Groups, Part I, Trans. Math. Monographs, vol. 172, American Mathematical Society, Providence, RI, USA, 1997

[3] J.H. Conway; R.T. Curtis; S.P. Norton; R.A. Parker; R.A. Wilson Atlas of Finite Groups, Oxford University Press, 1985

[4] M.R. Darafsheh; A. Iranmanesh; S.A. Moosavi Groups whose non-linear irreducible characters are rational valued, Arch. Math. (Basel), Volume 94 (2010) no. 5, pp. 411-418

[5] W. Feit; G.M. Seitz On finite rational groups and related topics, Ill. J. Math., Volume 33 (1988) no. 1, pp. 103-131

[6] I. Isaacs Character Theory of Finite Groups, Academic Press, 1976

[7] D. Kletzing Structure and Representations of Q-Groups, Lecture Notes in Mathematics, vol. 1084, Springer-Verlag, 1984

[8] M.L. Lewis The vanishing-off subgroups, J. Algebra, Volume 321 (2009), pp. 1313-1325

[9] M. Norooz-Abadian; H. Sharifi Sylow 2-subgroups of solvable $Q_{1}$ -groups, C. R. Acad. Sci. Paris, Ser. I (2016), pp. 1-4

[10] M. Norooz-Abadian, H. Sharifi, Some results about $Q_{1}$ -groups, in press.

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