On the normal subgroups and the factorization of some$\pi$-solvable irreducible linear groups
Trudy Instituta matematiki, Tome 29 (2021) no. 1, pp. 149-164

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For finite $\pi$-solvable absolutely irreducible linear group of degree $n=2|H|$ 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 normal subgroups and factorizations is proved.
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     title = {On the normal subgroups and the factorization of some$\pi$-solvable irreducible linear groups},
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A. A. Yadchenko. On the normal subgroups and the factorization of some$\pi$-solvable irreducible linear groups. Trudy Instituta matematiki, Tome 29 (2021) no. 1, pp. 149-164. http://geodesic.mathdoc.fr/item/TIMB_2021_29_1_a13/