Geodesic
On the solvability and factorization of some $\pi$-solvable irreducible linear groups of primary degree. Part I
Trudy Instituta matematiki, Tome 30 (2022) no. 1, pp. 84-98 
A. A. Yadchenko. On the solvability and factorization of some $\pi$-solvable irreducible linear groups of primary degree. Part I. Trudy Instituta matematiki, Tome 30 (2022) no. 1, pp. 84-98. http://geodesic.mathdoc.fr/item/TIMB_2022_30_1_a8/
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     title = {On the solvability and factorization of some $\pi$-solvable irreducible linear groups of primary degree. {Part~I}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The article begins a series of papers where for a set $\pi$ of odd primes $\pi$-solvable finite irreducible complex linear groups of degree $2|H|+1$ whose Hall $\pi$-subgroups are $TI$-subgroups and are not normal in groups. The goal of this series is to prove the solvability and determine the factorization of such groups. Proof of the theorem started. Preliminary results are obtained and some properties of minimal counterexample to the theorem are established.

[1] 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 | Zbl

[2] 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 | Zbl

[3] 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 | Zbl

[4] Yadchenko A. A., “O faktorizatsii nekotorykh $\Pi$-razreshimykh neprivodimykh lineinykh grupp”, Trudy Instituta matematiki NAN Belarusi, 27:1 (2019), 79–107 | MR

[5] Yadchenko A. A., “O normalnykh podgruppakh i faktorizatsii nekotorykh $\pi$-razreshimykh neprivodimykh lineinykh grupp”, Trudy Instituta matematiki NAN Belarusi, 29:1-2 (2021), 149–164

[6] Winter D.L., “On the Structure of Certain p-Solvable Linear Groups II”, J. of Algebra, 33 (1975), 170–190 | DOI | MR | Zbl

[7] Gorenstein D., Finite groups, Harper and Row, New York, 1968 | MR | Zbl

[8] Isaacs I.M., Character theory of finite groups, Academic Press, New York, 1976 | MR | Zbl

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

[10] Khosravi A., Khosravi B., “A new characterization of some alternating and symmetric groups. II”, International Journal of Mathematics and Mathematical Sciences, 30:4 (2004), 953–967 | MR | Zbl

[11] Crescenzo P., “A Diophantine equation which arises in the theory of finite groups”, Advances in Mathematics, 17:1 (1975), 25–29 | DOI | MR | Zbl

[12] Chunikhin S. A., Podgruppy konechnykh grupp, Nauka i tekhnika, Minsk, 1964 | MR

[13] Starostin A. I., “O gruppakh Frobeniusa”, Ukr. mat. zhurnal, 23:3 (1971), 629–639 | MR | Zbl

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

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

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