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Sib. Èlektron. Mat. Izv., 2008, Volume 5, Pages 20–24 (Mi semr88)  

This article is cited in 5 scientific papers (total in 5 papers)

Research papers

Insolubility of finite groups which are isospectral to the alternating group of degree $10$

A. M. Staroletov


Abstract: Let $G$ be a finite group and $\omega(G)$ the set of all element orders of $G$. We prove that if $\omega(G)=\omega(A_{10})$ where $G$ is a finite group, then $G$ is not-soluble.

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Document Type: Article
UDC: 512.5
MSC: 20D06
Received September 10, 2008, published February 21, 2008

Citation: A. M. Staroletov, “Insolubility of finite groups which are isospectral to the alternating group of degree $10$”, Sib. Èlektron. Mat. Izv., 5 (2008), 20–24

Citation in format AMSBIB
\Bibitem{Sta08}
\by A.~M.~Staroletov
\paper Insolubility of finite groups which are isospectral to the alternating group of degree~$10$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2008
\vol 5
\pages 20--24
\mathnet{http://mi.mathnet.ru/semr88}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2586619}


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    This publication is cited in the following articles:
    1. A. V. Zavarnitsine, “A solvable group isospectral to $\mathrm S_4(3)$”, Siberian Math. J., 51:1 (2010), 20–24  mathnet  crossref  mathscinet  isi
    2. A. M. Staroletov, “Groups isospectral to the degree 10 alternating group”, Siberian Math. J., 51:3 (2010), 507–514  mathnet  crossref  mathscinet  zmath  isi
    3. Kondratev A.S., “O konechnykh gruppakh s nebolshim prostym spektrom”, Matematicheskii forum (itogi nauki. yug Rossii), 6 (2012), 56–74  elib
    4. A. S. Kondrat'ev, “Finite groups that have the same prime graph as the group $A_{10}$”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 99–107  mathnet  crossref  mathscinet  isi  elib
    5. V. D. Mazurov, “$2$-Frobenius groups isospectral to the simple group $U_3(3)$”, Siberian Math. J., 56:6 (2015), 1108–1113  mathnet  crossref  crossref  mathscinet  isi  elib
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