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 Trudy Inst. Mat. i Mekh. UrO RAN, 2008, Volume 14, Number 2, Pages 143–163 (Mi timm31)

Algebra and Topology

On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. I

V. A. Belonogov

Abstract: The hypothesis that the alternating groups $A_n$ have no pairs of semiproportional irreducible characters is reduced to a hypothesis concerning the problem of describing the pairs of irreducible characters of the symmetric group $S_n$ that are semiproportional on one of the sets $A_n$ or $S_n\setminus A_n$. The form of this hypothesis (in contrast to the form of the original one) is maximally adapted for an inductive proof. Properties of a pair of the mentioned characters are expressed in terms of the structure of Young's diagrams for these characters. The theorem proved in this paper refines the structure of these diagrams in one of the two possible cases.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2008, 263, suppl. 2, S150–S171

Bibliographic databases:

UDC: 512.54

Citation: V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. I”, Trudy Inst. Mat. i Mekh. UrO RAN, 14, no. 2, 2008, 143–163; Proc. Steklov Inst. Math. (Suppl.), 263, suppl. 2 (2008), S150–S171

Citation in format AMSBIB
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\by V.~A.~Belonogov
\paper On irreducible characters of the group~$S_n$ that are semiproportional on~$A_n$ or $S_n\setminus A_n$.~I
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2008
\vol 14
\issue 2
\pages 143--163
\mathnet{http://mi.mathnet.ru/timm31}
\zmath{https://zbmath.org/?q=an:1175.20011}
\elib{http://elibrary.ru/item.asp?id=11929736}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2008
\vol 263
\issue , suppl. 2
\pages S150--S171
\crossref{https://doi.org/10.1134/S008154380806014X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-60949087215}

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This publication is cited in the following articles:
1. V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. II”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S60–S71
2. V. A. Belonogov, “O neprivodimykh kharakterakh gruppy $S_n$, poluproportsionalnykh na $A_n$ ili na $S_n\setminus A_n$. III”, Tr. IMM UrO RAN, 14, no. 4, 2008, 12–30
3. V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. IV.”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S10–S32
4. V. A. Belonogov, “O neprivodimykh kharakterakh gruppy $S_n$, poluproportsionalnykh na $A_n$ ili na $S_n\setminus A_n$. V”, Tr. IMM UrO RAN, 16, no. 2, 2010, 13–34
5. V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. VI”, Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S14–S35
6. Belonogov V.A., “On character tables and abstract structure of finite groups”, Character Theory of Finite Groups, Contemporary Mathematics, 524, 2010, 1–10
7. V. A. Belonogov, “O neprivodimykh kharakterakh gruppy $S_n$, poluproportsionalnykh na $A_n$ ili na $S_n\setminus A_n$. VII”, Tr. IMM UrO RAN, 17, no. 1, 2011, 3–16
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