On the solvability and factorization of some $\pi$-solvable irreducible linear groups of primary degree. Part III
Trudy Instituta matematiki, Tome 31 (2023) no. 2, pp. 91-102.

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The article is the third one in a series of papers, where for a set $\pi$ consisting of odd primes, finite $\pi$-solvable irreducible complex linear groups of degree $2|H|+1$ are investigated, for which Hall $\pi$-subgroups are $TI$-subgroups and are not normal in groups. The purpose of the series is to prove solvability and to determine the conditions for factorization of such groups. The proof of the theorem is continued. Further properties of the minimal counterexample to the theorem are established.
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A. A. Yadchenko. On the solvability and factorization of some $\pi$-solvable irreducible linear groups of primary degree. Part III. Trudy Instituta matematiki, Tome 31 (2023) no. 2, pp. 91-102. http://geodesic.mathdoc.fr/item/TIMB_2023_31_2_a9/

[1] Yadchenko A. A., “O razreshimosti i faktorizatsii nekotorykh $\pi$-razreshimykh neprivodimykh lineinykh grupp primarnoi stepeni. Chast I”, Tr. In-ta matematiki, 30:1–2 (2022), 84–98 | Zbl

[2] Yadchenko A. A., “O razreshimosti i faktorizatsii nekotorykh $\pi$-razreshimykh neprivodimykh lineinykh grupp primarnoi stepeni. Chast II”, Tr. In-ta matematiki, 31:1 (2023), 77–89 | MR

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

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

[5] Yadchenko A. A., “O $\Pi$-razreshimykh neprivodimykh lineinykh gruppakh s khollovoi $TI$-podgruppoi nechetnogo poryadka. II”, Tr. In-ta matematiki, 17:2 (2009), 94–104 | Zbl

[6] Romanovskii A. V., Yadchenko A. A., “O silovskikh podgruppakh lineinykh grupp”, Matematicheskii sb., 137:4(12) (1988), 568–573 | Zbl

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

[8] Yadchenko A. A., “O spektrakh $p$-elementov konechnykh kompleksnykh $p$-razreshimykh lineinykh grupp”, Matematicheskie zametki, 50:3 (1991), 143–151 | MR | Zbl

[9] Yadchenko A. A., “O $\pi$-razreshimykh neprivodimykh lineinykh gruppakh skhollovoi $TI$-podgruppoi nechetnogo poryadka I”, Tr. In-ta matematiki, 16:2 (2008), 118–130 | Zbl

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

[11] Yadchenko A. A., “Razreshimye neprivodimye lineinye gruppy proizvolnoi stepeni s khollovskoi TI-podgruppoi”, Matematicheskie zametki, 48:2 (1990), 137–144 | MR | Zbl

[12] Yadchenko A. A., “O faktorizatsii nekotorykh $\pi$-razreshimykh neprivodimykh lineinykh grupp”, Tr. In-ta matematiki, 27:1–2 (2019), 79–107 | MR

[13] Yadchenko A. A., “O normalnykh podgruppakh i faktorizatsii nekotorykh $\pi$-razreshimykh neprivodimykh lineinykh grupp”, Tr. In-ta matematiki, 29:1–2 (2021), 149–164 | Zbl