no. 1
Group theory
Sylow 2-subgroups of solvable Q1-groups
[2-Sous-groupes de Sylow des Q1-groupes résolubles]

Présenté par : the Editorial Board

Norooz-Abadian, Meysam1 ; Sharifi, Hesamuddin1
1 Department of Mathematics, Faculty of Science, Shahed University, Tehran, Iran
Comptes Rendus. Mathématique, Tome 355 (2017) no. 1, pp. 20-23.

Un groupe fini dont les caractères complexes non linéaires sont rationnels est appelé un Q1-groupe. Nous étudions dans cette Note la structure d'un Q1-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 Q1-group. In this paper, we study the structure of a Q1-group through its Sylow 2-subgroups.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.11.001
Norooz-Abadian, Meysam 1 ; Sharifi, Hesamuddin 1

1 Department of Mathematics, Faculty of Science, Shahed University, Tehran, Iran 
@article{CRMATH_2017__355_1_20_0,
     author = {Norooz-Abadian, Meysam and Sharifi, Hesamuddin},
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2016.11.001/}
}
TY  - JOUR
AU  - Norooz-Abadian, Meysam
AU  - Sharifi, Hesamuddin
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
UR  - http://www.numdam.org/articles/10.1016/j.crma.2016.11.001/
DO  - 10.1016/j.crma.2016.11.001
LA  - en
ID  - CRMATH_2017__355_1_20_0
ER  - 
%0 Journal Article
%A Norooz-Abadian, Meysam
%A Sharifi, Hesamuddin
%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
%U http://www.numdam.org/articles/10.1016/j.crma.2016.11.001/
%R 10.1016/j.crma.2016.11.001
%G en
%F CRMATH_2017__355_1_20_0
Norooz-Abadian, Meysam; Sharifi, Hesamuddin. Sylow 2-subgroups of solvable $ {\mathbb{Q}}_{1}$-groups. Comptes Rendus. Mathématique, Tome 355 (2017) no. 1, pp. 20-23. doi : 10.1016/j.crma.2016.11.001. http://www.numdam.org/articles/10.1016/j.crma.2016.11.001/

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

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

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

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

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

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

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

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

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

[10] Norooz-Abadian, M.; Sharifi, H. Frobenius Q1-groups, Arch. Math. (Basel), Volume 105 (2015), pp. 509-517

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

Cité par Sources :