Sylow 2-subgroups of solvable $ {\mathbb{Q}}_{1}$-groups

Meysam Norooz-Abadian; Hesamuddin Sharifi

doi:10.1016/j.crma.2016.11.001

Group theory

Sylow 2-subgroups of solvable

Q_{1}

-groups
[2-Sous-groupes de Sylow des

Q_{1}

-groupes résolubles]

Présenté par : the Editorial Board

Meysam Norooz-Abadian ¹ ; Hesamuddin Sharifi ¹

¹ Department of Mathematics, Faculty of Science, Shahed University, Tehran, Iran

Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 20-23.

Résumé
Abstract

Un groupe fini dont les caractères complexes non linéaires sont rationnels est appelé un $Q_{1}$ -groupe. Nous étudions dans cette Note la structure d'un $Q_{1}$ -groupe par le biais de ses 2-sous-groupes de Sylow.

A finite group whose irreducible complex non-linear characters are rational is called a $Q_{1}$ -group. In this paper, we study the structure of a $Q_{1}$ -group through its Sylow 2-subgroups.

Reçu le : 2016-03-23
Accepté le : 2016-11-08
Publié le : 2016-11-23

DOI : 10.1016/j.crma.2016.11.001

Affiliations des auteurs :

Meysam Norooz-Abadian ¹ ; Hesamuddin Sharifi ¹

¹ Department of Mathematics, Faculty of Science, Shahed University, Tehran, Iran

@article{CRMATH_2017__355_1_20_0,
     author = {Meysam Norooz-Abadian and Hesamuddin Sharifi},
     title = {Sylow 2-subgroups of solvable $ {\mathbb{Q}}_{1}$-groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {20--23},
     publisher = {Elsevier},
     volume = {355},
     number = {1},
     year = {2017},
     doi = {10.1016/j.crma.2016.11.001},
     language = {en},
}

TY  - JOUR
AU  - Meysam Norooz-Abadian
AU  - Hesamuddin Sharifi
TI  - Sylow 2-subgroups of solvable $ {\mathbb{Q}}_{1}$-groups
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 20
EP  - 23
VL  - 355
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crma.2016.11.001
LA  - en
ID  - CRMATH_2017__355_1_20_0
ER  -

%0 Journal Article
%A Meysam Norooz-Abadian
%A Hesamuddin Sharifi
%T Sylow 2-subgroups of solvable $ {\mathbb{Q}}_{1}$-groups
%J Comptes Rendus. Mathématique
%D 2017
%P 20-23
%V 355
%N 1
%I Elsevier
%R 10.1016/j.crma.2016.11.001
%G en
%F CRMATH_2017__355_1_20_0

Meysam Norooz-Abadian; Hesamuddin Sharifi. Sylow 2-subgroups of solvable $ {\mathbb{Q}}_{1}$-groups. Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 20-23. doi : 10.1016/j.crma.2016.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.11.001/

Bibliographie
Cité par

[1] 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

[2] M.R. Darafsheh; H. Sharifi Sylow 2-subgroups of solvable $Q$ -groups, Extr. Math., Volume 22 (2007) no. 1, pp. 83-91

[3] S. Dolfi; E. Pacifici; L. Sanus; P. Spiga On the orders of zeros of irreducible characters, J. Algebra, Volume 321 (2009), pp. 345-352

[4] E. Farias e Soares Big primes and character values for solvable groups, J. Algebra, Volume 100 (1986), pp. 305-324

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

[6] I.M. Isaacs Finite Group Theory, American Mathematical Society, 2008

[7] M. Isaacs; G. Navarro Sylow 2-subgroups of rational groups, Math. Z., Volume 272 (2012) no. 3–4, pp. 937-945

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

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

[10] M. Norooz-Abadian; H. Sharifi Frobenius $Q_{1}$ -groups, Arch. Math. (Basel), Volume 105 (2015), pp. 509-517

[11] J.G. Thompson Normal p-complements and irreducible characters, J. Algebra, Volume 14 (1970), pp. 129-134

Cité par Sources :

Commentaires - Politique