Geodesic
On the factorization of some $\pi$-solvable irreducible linear groups
Trudy Instituta matematiki, Tome 27 (2019) no. 1, pp. 79-107.

Voir la notice de l'article provenant de la source Math-Net.Ru

For finite $\pi$-solvable absolutely irreducible linear group of degree $n2|H|$ over a field of zero characteristic with a $\pi$-Hall $TI$-subgroup $H$ of a odd order that is not normal, the existence of certain factorizations is proved. 
@article{TIMB_2019_27_1_a8,
     author = {A. A. Yadchenko},
     title = {On the factorization of some $\pi$-solvable irreducible linear groups},
     journal = {Trudy Instituta matematiki},
     pages = {79--107},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2019_27_1_a8/}
}
TY  - JOUR
AU  - A. A. Yadchenko
TI  - On the factorization of some $\pi$-solvable irreducible linear groups
JO  - Trudy Instituta matematiki
PY  - 2019
SP  - 79
EP  - 107
VL  - 27
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2019_27_1_a8/
LA  - ru
ID  - TIMB_2019_27_1_a8
ER  - 
%0 Journal Article
%A A. A. Yadchenko
%T On the factorization of some $\pi$-solvable irreducible linear groups
%J Trudy Instituta matematiki
%D 2019
%P 79-107
%V 27
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2019_27_1_a8/
%G ru
%F TIMB_2019_27_1_a8
A. A. Yadchenko. On the factorization of some $\pi$-solvable irreducible linear groups. Trudy Instituta matematiki, Tome 27 (2019) no. 1, pp. 79-107. http://geodesic.mathdoc.fr/item/TIMB_2019_27_1_a8/

[1] Okuyama T., “On finite groups whose Sylow $p$-subgroup is a T.I. set”, Hokkaido Math. J., 4:2 (1975), 303–305

[2] Yadchenko A. A., “O konechnykh $\pi$-razreshimykh lineinykh gruppakh”, Arifmeticheskoe i podgruppovoe stroenie konechnykh grupp, Nauka i tekhnika, Minsk, 1986, 181–207

[3] Yadchenko A. A., “Razreshimye neprivodimye lineinye gruppy proizvolnoi stepeni s khollovskoi TI-podgruppoi”, Matem. zametki, 48 (1990), 137–144

[4] Yadchenko A. A., “O $\Pi$-razreshimykh neprivodimykh lineinykh gruppakh s khollovoi $TI -$podgruppoi nechetnogo poryadka I”, Trudy Instituta matematiki NAN Belarusi, 16:2 (2008), 118–130

[5] Yadchenko A. A., “O $\Pi$-razreshimykh neprivodimykh lineinykh gruppakh s khollovoi $TI -$podgruppoi nechetnogo poryadka II”, Trudy Instituta matematiki NAN Belarusi, 17:2 (2009), 94–104

[6] Yadchenko A. A., “O $\Pi$-razreshimykh neprivodimykh lineinykh gruppakh s khollovoi $TI -$podgruppoi nechetnogo poryadka III”, Trudy Instituta matematiki NAN Belarusi, 18:2 (2010), 99–114

[7] Yadchenko A. A., “O faktorizatsii $\pi$-razreshimykh neprivodimykh lineinykh grupp”, Doklady NAN Belarusi, 58:5 (2014), 5–11

[8] Yadchenko A.A., “On solvability of certain irreducible linear groups”, Asian Journal of Mathematics and Computer Research, 5:1 (2015), 20–37

[9] Yadchenko A.A., “K probleme Aizeksa”, Matem. sbornik, 204:12 (2013), 147–156

[10] Gorenstein D., Finite groups, Harper and Row, New York, 1968

[11] Isaacs I.M., Character theory of finite groups, Academic Press, New York, 1976

[12] Yadchenko A.A., “Ob avtomorfizmakh i normalnykh khollovskikh podgruppakh lineinykh grupp”, Vestsi NAN Belarusi. Seryya fiz.-mat. navuk, 2007, no. 3, 49–54

[13] Glauberman G., “Correspodences of characters for relatively prime operator groups”, Canad. J. Math., 20 (1968), 1465–1488

[14] Chunikhin S. A., Podgruppy konechnykh grupp, Nauka i tekhnika, Minsk, 1964

[15] Starostin A. I., “O gruppakh Frobeniusa”, Ukr. matem. zhurnal, 23:3 (1971), 629–639

[16] Belonogov V. A., Fomin A. N., Matrichnye predstavleniya v teorii konechnykh grupp, Nauka, M., 1976

[17] Romanovskii A. A., Yadchenko A. A., “O silovskikh podgruppakh lineinykh grupp”, Matem. sbornik, 137:4 (12) (1988), 568–573

[18] Dixon J., The structure of linear groups, Butler and Tanner Ltd, L., 1971

[19] Yadchenko A. A., Romanovskii A. V., “K problemme Aizeksa o konechnykh $p$-razreshimykh lineinykh gruppakh”, Matem. zametki, 69 (2001), 144–152

[20] Yadchenko A.A., “O normalnykh khollovskikh podgruppakh $\Pi$-obosoblennykh lineinykh grupp”, Vestsi NAN Belarusi. Seryya fiz.-matem. navuk, 2005, no. 1, 35–39