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Sugimoto, Masahiro. (1403). Harada's conjecture II for the finite general linear groups and unitary groups. , 14(4), 285-296. doi: 10.22108/ijgt.2024.140888.1896
Masahiro Sugimoto. "Harada's conjecture II for the finite general linear groups and unitary groups". , 14, 4, 1403, 285-296. doi: 10.22108/ijgt.2024.140888.1896
Sugimoto, Masahiro. (1403). 'Harada's conjecture II for the finite general linear groups and unitary groups', , 14(4), pp. 285-296. doi: 10.22108/ijgt.2024.140888.1896
Sugimoto, Masahiro. Harada's conjecture II for the finite general linear groups and unitary groups. , 1403; 14(4): 285-296. doi: 10.22108/ijgt.2024.140888.1896

Harada's conjecture II for the finite general linear groups and unitary groups

International Journal of Group Theory
دوره 14، شماره 4، اسفند 2025، صفحه 285-296    اصل مقاله (473.26 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2024.140888.1896
نویسنده
Masahiro Sugimoto*
Department of Mathematics, University of Tsukuba 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577 Japan
چکیده
K. Harada conjectured for any finite group $G$, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when $G$ is the general linear group over a finite field. We show the conjecture holds if the order of the field is sufficiently large.
کلیدواژه‌ها
irreducible character؛ conjugacy classes؛ partitions
مراجع

[1] T. Abe and N. Chigira, Towards a solution to Harada’s conjecture II, RIMS Kokyuroku, 2189 (2021) 77–86.
[2] V. Ennola,On the characters of the finite unitary groups, Ann. Acad. Sci. Fenn. Ser. A I, 323 (1963) 35 pp.
[3] V. Ennola, On the conjugacy classes of the finite unitary groups, Ann. Acad. Sci. Fenn. Ser. A I, 313 (1962) 13 pp.
[4] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.12.2, 2022, https://www.gap-system.org
[5] J. A. Green, The characters of the finite general linear groups, Trans. Amer. Math. Soc., 80 (1955) 402–447.
[6] K. Harada, Revisiting character theory of finite groups, Bull. Inst. Math. Acad. Sin. (N.S.), 13 no. 4 (2018) 383–395.
[7] A. Hida, Harada’s conjecture on character degrees and class sizes –symmetric and alternating groups–, RIMS Kokyuroku, 2086 (2018) 144–153.
[8] N. Kawanaka, Generalized Gelfand-Graev representations and Ennola duality, Algebraic groups and related topics (Kyoto/Nagoya, 1983), Adv. Stud. Pure Math., North-Holland, Amsterdam, 1985 175–206.

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