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Algebra Logika, 2008, Volume 47, Number 2, Pages 135–156 (Mi al351)  

This article is cited in 10 scientific papers (total in 10 papers)

Irreducible characters of the group $S_n$ that are semiproportional on $A_n$

V. A. Belonogov

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

Abstract: Previously, we dubbed the conjecture that the alternating group An has no semiproportional irreducible characters for any natural $n$ [1]. This conjecture was then shown to be equivalent to the following [3]. Let $\alpha$ and $\beta$ be partitions of a number $n$ such that their corresponding characters $\chi^\alpha$ and $\chi^\beta$ in the group $S_n$ are semiproportional on $A_n$. Then one of the partitions $\alpha$ or $\beta$ is self-associated. Here, we describe all pairs $(\alpha,\beta)$ of partitions satisfying the hypothesis and the conclusion of the latter conjecture.

Keywords: alternating group, irreducible character, semiproportional characters.

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English version:
Algebra and Logic, 2008, 47:2, 77–90

Bibliographic databases:

UDC: 512.54
Received: 28.02.2007

Citation: V. A. Belonogov, “Irreducible characters of the group $S_n$ that are semiproportional on $A_n$”, Algebra Logika, 47:2 (2008), 135–156; Algebra and Logic, 47:2 (2008), 77–90

Citation in format AMSBIB
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\by V.~A.~Belonogov
\paper Irreducible characters of the group $S_n$ that are semiproportional on~$A_n$
\jour Algebra Logika
\yr 2008
\vol 47
\issue 2
\pages 135--156
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2438006}
\zmath{https://zbmath.org/?q=an:1155.20010}
\transl
\jour Algebra and Logic
\yr 2008
\vol 47
\issue 2
\pages 77--90
\crossref{https://doi.org/10.1007/s10469-008-9004-2}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  elib
    2. V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. I”, Proc. Steklov Inst. Math. (Suppl.), 263, suppl. 2 (2008), S150–S171  mathnet  crossref  zmath  isi  elib
    3. 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  mathnet  crossref  mathscinet  isi  elib
    4. 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  mathnet  elib
    5. 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  mathnet  crossref  isi  elib
    6. 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
    7. 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
    8. Belonogov V.A., “On character tables and abstract structure of finite groups”, Character Theory of Finite Groups, Contemporary Mathematics, 524, 2010, 1–10  crossref  mathscinet  zmath  isi
    9. 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
    10. Z. Momen, B. Khosravi, “On recognizability of $\operatorname{PSU}_3(q)$ by the orders of maximal abelian subgroups”, Siberian Math. J., 60:1 (2019), 124–139  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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