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 Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 1, Pages 3–16 (Mi timm667)

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

V. A. Belonogov

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

Abstract: The proof of Hypothesis A, which was introduced in the first paper with the same title, was carried out in the previous six papers of the series and is completed in the present paper. As a consequence of this hypothesis, the following theorem is obtained: the alternating group $A_n$ for any natural $n$ has no pairs of semiproportional irreducible characters. The suggestion about the validity of this theorem was first formulated in the author's paper in 2004.

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

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UDC: 512.54

Citation: V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. VII”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 1, 2011, 3–16

Citation in format AMSBIB
\Bibitem{Bel11} \by V.~A.~Belonogov \paper On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~VII \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2011 \vol 17 \issue 1 \pages 3--16 \mathnet{http://mi.mathnet.ru/timm667} \elib{http://elibrary.ru/item.asp?id=17869778} 

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This publication is cited in the following articles:
1. V. A. Belonogov, “Small interactions in the groups $\mathrm{Sp}_4(q)$ for even $q$”, Proc. Steklov Inst. Math. (Suppl.), 279, suppl. 1 (2012), 23–42
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