Degrees of irreducible components of permutation character and normal subgroups of a finite group
https://doi.org/10.67268/1812-5093-2026-34-1-39-44
EDN: UVLPLF
Abstract
For an odd prime number $r$, we found conditions under which a Sylow $r$-subgroup $G_{r}$ is Abelian and normal in an irreducible complex linear group $G$.
About the Author
A. A. Yadchenko
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
References
1. Ito N. On the theorem of N. F. Blichfeldt. Nagoya Math. J., 1953, vol. 15, pp. 75–77.
2. Winter D. L. On finite solvable linear groups. Ill. J. Math., 1971, vol. 15, no. 3, pp. 425–428.
3. Winter D. L. Solvability of certain p-solvable linear groups of finite order. Pacific J. Math., 1970, vol. 34, no. 3, pp. 827–835.
4. Isaacs I. M. Complex p-solvable linear groups. J. Algebra, 1973, vol. 24, no. 3, pp. 513–530.
5. Winter D. L. On the structure of certain p-solvable linear groups. J. Algebra, 1974, vol. 31, no. 3, pp. 543–546.
6. Yadchenko A. A., Romanovskii A. V. On the Isaacs problem concerning finite p -solvable linear groups. Math. Notes, 2001, vol. 69, no. 1, pp. 144–152 (in Russian).
7. Newton B. On the degrees of complex p-solvable linear groups. J. Algebra, 2005, vol. 288, pp. 384–391.
8. Yadchenko A. A. On Isaacs’ problem. Math. Sbornik, 2013, vol. 204, no. 12, pp. 1839–1848.
9. Romanovskii A. V., Yadchenko A. A. Monomial characters and normal subgroup of finite groups. Ukr. Math. J., 1991, vol. 43, no. 7–8, pp. 925–929.
10. Gorenstein D. Finite Groups. New York, Harper and Row, 1968. 527 p.
11. Isaacs I. M. Character Theory of Finite Groups. New York, Academic Press, 1976. 303 p.
12. Chunihin S. A. Subgroup of Finite Groups. Minsk, Nauka i Tekhnika, 1975. 158 p.
13. Arad Z., Ward M. B. New criteria for the solvability of finite groups. J. Algebra, 1982, vol. 77, no. 1, pp. 234–246.
14. Conway J. H. Atlas of finite groups. London, Clarendon Press, 1985. 252 p.
Review
For citations:
Yadchenko A.A. Degrees of irreducible components of permutation character and normal subgroups of a finite group. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2026;34(1):39-44. (In Russ.) https://doi.org/10.67268/1812-5093-2026-34-1-39-44. EDN: UVLPLF
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