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On the solvability and factorization of some π-solvable irreducible linear groups of primary degree. Part V

Abstract

The work is the fifth and final one in a series of articles, 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.

About the Author

A. A. Yadchenko
Institute of Mathematics of the National Academy of Sciences of Belarus
Russian Federation

Minsk



References

1. Yadchenko A. A. On the solvability and factorization of some ?-solvable irreducible linear groups of primary degree. Part I. Trudy Instituta mathematiki, 2022, vol. 30, no. 1–2, pp. 84–98 (in Russian).

2. Yadchenko A. A. On the solvability and factorization of some ?-solvable irreducible linear groups of primary degree. Part II. Trudy Instituta mathematiki, 2023, vol. 31, no. 1, pp. 77–89 (in Russian).

3. Yadchenko A. A. On the solvability and factorization of some ?-solvable irreducible linear groups of primary degree. Part III. Trudy Instituta mathematiki, 2023, vol. 31, no. 2, pp. 91–102 (in Russian).

4. Yadchenko A. A. On the solvability and factorization of some ?-solvable irreducible linear groups of primary degree. Part IV. Proceedings of the Institute of Mathematics of the NAS of Belarus, 2024, vol. 32, no. 2, pp. 17–30 (in Russian).

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9. Yadchenko A. A. On the ?-solvable irreducible linear groups with Hall TI-subgrops of odd order I. Trudy Instituta mathematiki, 2008, vol. 16, no. 2, pp. 118–130 (in Russian).

10. Yadchenko A. A. On the normal subgroups and factorization some ?-solvable irreducible linear groups. Trudy Instituta mathematiki, 2021, vol. 29, no. 1–2, pp. 149–164 (in Russian).

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For citations:


Yadchenko A.A. On the solvability and factorization of some π-solvable irreducible linear groups of primary degree. Part V. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2025;33(1):44-57. (In Russ.)

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ISSN 1812-5093 (Print)