On the semiproportional character conjecture
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Two characters of a finite group G are semiproportional if they are not proportional and G is a union of two disjoint normal subsets such that the restrictions of these characters to each of the subsets are proportional. We obtain some results on the structure of an arbitrary finite group having a pair of semiproportional irreducible characters; in particular, assertions on the order of the group and on the kernels of semiproportional characters. We also consider the following conjecture: Semiproportional irreducible characters of a finite group have equal degrees. We validate this conjecture for 2-decomposable groups and prove that if the conjecture holds for two groups then it holds for their direct product.
Keywordsfinite groups irreducible characters Semiproportional Character Conjecture D-blocks
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- 1.Belonogov V. A., “D-Blocks of characters of finite groups,” Amer. Math. Soc. Transl. (2), 143, 103–128 (1989).Google Scholar
- 2.Belonogov V. A., Representations and Characters in the Theory of Finite Groups [in Russian], Akad. Nauk SSSR, Ural0sk. Otdel., Sverdlovsk (1990).Google Scholar
- 3.Belonogov V. A., “Interactions and D-blocks in finite groups,” in: Subgroup Structure of Groups [in Russian], Ural Otdel. Akad. Nauk SSSR, Sverdlovsk, 1988, pp. 4–44.Google Scholar
- 4.Belonogov V. A., “On small interactions in finite groups,” Trudy Inst. Mat. Mekh. Ural Otdel. Ross. Akad. Nauk, 2, 3–18 (1992).Google Scholar
- 5.Belonogov V. A., “Small interactions in the groups GL3(q), GU3(q), PGL3(q), and PGU3(q),” Trudy Inst. Mat. Mekh. Ural Otdel. Ross. Akad. Nauk, 4, 17–47 (1996).Google Scholar
- 6.Belonogov V. A., “Small interactions in the groups SL3(q), SU3(q), PSL3(q), and PSU3(q),” Trudy Inst. Mat. Mekh. Ural Otdel. Ross. Akad. Nauk, 5, 3–27 (1998).Google Scholar
- 7.Belonogov V. A., “On the irreducible characters of the groups S n and A n,” Sibirsk. Mat. Zh., 45, No.5, 977–994 (2004).Google Scholar
- 8.Isaacs I. M., Character Theory of Finite Groups, Acad. Press, New York (1976).Google Scholar
- 9.Belonogov V. A., “A property of the character table for a finite group,” Algebra i Logika, 39, No.3, 273–279 (2000).Google Scholar
- 10.Huppert B. and Blackburn N., Finite Groups. II, Springer-Verlag, Berlin etc. (1982).Google Scholar