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 Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 3, Pages 45–60 (Mi timm574)

On the structure of finite groups isospectral to an alternating group

I. A. Vakula

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

Abstract: It is proved that every finite group isospectral to an alternating group $A_n$ of degree $n$ greater than 21 has a chief factor isomorphic to an alternating group $A_k$, where $k\le n$ and the half-interval $(k,n]$ contains no primes.

Keywords: finite groups, alternating groups, spectrum of a group, isospectral groups, chief factors.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 1, S271–S286

Bibliographic databases:

UDC: 512.542.52

Citation: I. A. Vakula, “On the structure of finite groups isospectral to an alternating group”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 3, 2010, 45–60; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S271–S286

Citation in format AMSBIB
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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. I. B. Gorshkov, “Thompson's conjecture for simple groups with connected prime graph”, Algebra and Logic, 51:2 (2012), 111–127
2. I. B. Gorshkov, “Recognizability of alternating groups by spectrum”, Algebra and Logic, 52:1 (2013), 41–45
3. I. B. Gorshkov, “Recognizability of symmetric groups by spectrum”, Algebra and Logic, 53:6 (2015), 450–457
4. A. Mahmoudifar, B. Khosravi, “On characterization by order and prime graph for alternating groups”, Siberian Math. J., 56:1 (2015), 125–131
5. I. B. Gorshkov, “On Thompson's conjecture for alternating and symmetric groups of degree greater than 1361”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 58–65
6. Gorshkov I.B., Grishkov A.N., “On Recognition By Spectrum of Symmetric Groups”, Sib. Electron. Math. Rep., 13 (2016), 111–121
7. Babai A. Mahmoudifa A., “Thompson'S Conjecture For the Alternating Group of Degree 2&Itp&It and 2&Itp&It+1”, Czech. Math. J., 67:4 (2017), 1049–1058
8. Gorshkov I.B., “On Thompson'S Conjecture For Alternating Groups of Large Degree”, J. Group Theory, 20:4 (2017), 719–728
9. Gorshkov I., Staroletov A., “On Groups Having the Prime Graph as Alternating and Symmetric Groups”, Commun. Algebr., 47:9 (2019), 3905–3914
10. Gorshkov I.B., “Thompson'S Conjecture For Alternating Groups”, Commun. Algebr., 47:1 (2019), 30–36
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