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 Trudy Inst. Mat. i Mekh. UrO RAN, 2007, Volume 13, Number 1, Pages 11–43 (Mi timm69)

Certain pairs of irreducible characters of the groups $S_n$ and $A_n$

V. A. Belonogov

Abstract: Investigation of pairs of semiproportional irreducible characters of finite groups is continued. The interest in these investigations is maintained by the discovered earlier connection between the presence or absence of such a pair in a group and the local structure of this group. In the paper, the question of the presence of such pairs in the alternating groups $A_n$ is investigated. A more general problem of description of pairs of irreducible characters of the symmetric group $S_n$ having the same set of roots in one of the sets $A_n$ and $S_n\setminus A_n$ is also considered. All such pairs of irreducible characters of the symmetric group $S_n$ have been found in the case when the main diagonal lengths of the Young diagrams corresponding to these characters do not exceed 2.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2007, 257, suppl. 1, S10–S46

Bibliographic databases:

UDC: 512.54

Citation: V. A. Belonogov, “Certain pairs of irreducible characters of the groups $S_n$ and $A_n$”, Ãðóïïû è ãðàôû, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 1, 2007, 11–43; Proc. Steklov Inst. Math. (Suppl.), 257, suppl. 1 (2007), S10–S46

Citation in format AMSBIB
\Bibitem{Bel07} \by V.~A.~Belonogov \paper Certain pairs of irreducible characters of the groups $S_n$ and $A_n$ \inbook Ãðóïïû è ãðàôû \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2007 \vol 13 \issue 1 \pages 11--43 \mathnet{http://mi.mathnet.ru/timm69} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2338238} \elib{http://elibrary.ru/item.asp?id=12040750} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2007 \vol 257 \issue , suppl. 1 \pages S10--S46 \crossref{https://doi.org/10.1134/S0081543807050021} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547677911} 

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This publication is cited in the following articles:
1. V. A. Belonogov, “Young diagrams without hooks of length 4 and characters of the group $S_n$”, Proc. Steklov Inst. Math. (Suppl.), 261, suppl. 1 (2008), S24–S35
2. V. A. Belonogov, “Certain pairs of irreducible characters of the groups $S_n$”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S12–S34
3. V. A. Belonogov, “Irreducible characters of the group $S_n$ that are semiproportional on $A_n$”, Algebra and Logic, 47:2 (2008), 77–90
4. V. A. Belonogov, “The young diagrams of a pair of irreducible characters of $S_n$ with the same zero set on $S^\varepsilon_n$”, Siberian Math. J., 49:5 (2008), 784–795
5. V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. I”, Proc. Steklov Inst. Math. (Suppl.), 263, suppl. 2 (2008), S150–S171
6. 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
7. 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
8. 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
9. 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
10. 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
11. Belonogov V.A., “On character tables and abstract structure of finite groups”, Character Theory of Finite Groups, Contemporary Mathematics, 524, 2010, 1–10
12. 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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