Geodesic
On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. VII
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 3-16
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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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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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/TIMM_2011_17_1_a0/

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