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

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

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
\Bibitem{Bel08} \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 \mathnet{http://mi.mathnet.ru/al351} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000258151800001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-49249121063} 

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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
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
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
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
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
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
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
8. Belonogov V.A., “On character tables and abstract structure of finite groups”, Character Theory of Finite Groups, Contemporary Mathematics, 524, 2010, 1–10
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
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
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