Automorphisms and Normal Subgroups of Linear Groups
Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 469-476.

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In the present paper, the properties of orders of coprime automorphisms of irreducible linear groups are established and sufficient conditions for the existence of a normal Hall $\pi$-subgroup in a given $\pi$-separable irreducible complex linear group are obtained.
Keywords: finite group, irreducible linear group, coprime automorphism, normal Hall subgroup, irreducible character, Sylow group
Mots-clés : Frobenius group.
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A. A. Yadchenko. Automorphisms and Normal Subgroups of Linear Groups. Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 469-476. http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a13/

[1] D. L. Winter, “On the structure of certain $p$-solvable linear groups”, J. Algebra, 31:3 (1974), 543–546 | DOI | MR | Zbl

[2] I. M. Isaacs, “Complex $p$-solvable linear groups”, J. Algebra, 24:3 (1973), 513–530 | DOI | MR | Zbl

[3] A. A. Yadchenko, A. V. Romanovskii, “K probleme Aizeksa o konechnykh $p$-razreshimykh lineinykh gruppakh”, Matem. zametki, 69:1 (2001), 144–152 | MR | Zbl

[4] A. A. Yadchenko, “O normalnykh khollovskikh podgruppakh $\pi$-obosoblennykh lineinykh grupp”, Vestsi NAN Belarusi, 3:1 (2005), 35–39 | MR

[5] I. M. Isaacs, “Characters of solvable groups”, The Santa Cruz conference on finite groups (Univ. California, Santa Cruz, Calif., 1979), Proc. Sympos. Pure Math., 37, Amer. Math. Soc., Providence, R.I., 1980, 377–384 | MR | Zbl

[6] D. L. Winter, “On finite solvable linear groups”, Illinois J. Math., 15:3 (1971), 425–428 | MR | Zbl

[7] D. Gorenstein, Finite groups, Harper's Series in Modern Mathematics, Harper Row, New York–London, 1968 | MR | Zbl

[8] I. M. Isaacs, Character theory of finite groups, Pure Appl. Math. (N. Y.), 69, Academic Press, New York–London, 1976 | MR | Zbl

[9] G. Glauberman, “Correspondens of character for relativeli prime groups”, Canad. J. Math., 20 (1968), 1465–1488 | MR | Zbl

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

[11] A. V. Romanovskii, A. V. Yadchenko, “Monomialnye kharaktery i normalnye podgruppy konechnykh grupp”, Ukr. matem. zhurn., 43:7–8 (1991), 991–996 | MR | Zbl