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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 2, Pages 12–33 (Mi timm219)  

This article is cited in 3 scientific papers (total in 3 papers)

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

V. A. Belonogov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Investigations are continued concerning the conjecture that the alternating groups $A_n$ have no pairs of semiproportional irreducible characters. In order to prove this conjecture by induction on $n$, the author proposed a new conjecture, formulated in terms of pairs $\chi^\alpha$ and $\chi^\beta$ of irreducible characters of the symmetric group $S_n$ that are semiproportional on one of the sets $A_n$ or $S_n\setminus A_n$ ($\alpha$ and $\beta$ are partitions of the number $n$ corresponding to these characters). The theorem proved in this paper allows one to exclude from consideration the item of this conjecture in which the 4-kernels of the partitions $\alpha$ and $\beta$ have type $3^k.\Sigma_l$.

Keywords: symmetric groups, alternating groups, irreducible characters, semiproportionality

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 267, suppl. 1, S10–S32

Bibliographic databases:

UDC: 512.54
Received: 05.12.2008

Citation: V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. IV.”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 12–33; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S10–S32

Citation in format AMSBIB
\Bibitem{Bel09}
\by V.~A.~Belonogov
\paper On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~IV.
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 2
\pages 12--33
\mathnet{http://mi.mathnet.ru/timm219}
\elib{http://elibrary.ru/item.asp?id=12878765}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 267
\issue , suppl. 1
\pages S10--S32
\crossref{https://doi.org/10.1134/S0081543809070025}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000274041900002}


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    This publication is cited in the following articles:
    1. 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  mathnet  elib
    2. 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  mathnet  crossref  isi  elib
    3. 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  mathnet  elib
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