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Sibirsk. Mat. Zh., 2004, Volume 45, Number 6, Pages 1256–1262 (Mi smj1136)  

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

Recognition of the finite simple groups $F_4(2^m)$ by spectrum

A. V. Vasil'eva, M. A. Grechkoseevab, V. D. Mazurova, Kh. P. Chaoc, G. Yu. Chenc, W. Shid

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University, Mechanics and Mathematics Department
c Southwest China Normal University
d Soochow University

Abstract: The spectrum of a finite group is the set of its element orders. A finite group $G$ is said to be recognizable by spectrum, if every finite group with the same spectrum as $G$ is isomorphic to $G$. The purpose of the paper is to prove that for every natural $m$ the finite simple Chevalley group $F_4(2^m)$ is recognizable by spectrum.

Keywords: recognition by spectrum, finite simple group, group of Lie type

Full text: PDF file (220 kB)
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English version:
Siberian Mathematical Journal, 2004, 45:6, 1031–1035

Bibliographic databases:

UDC: 519.542
Received: 22.09.2004

Citation: A. V. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov, Kh. P. Chao, G. Yu. Chen, W. Shi, “Recognition of the finite simple groups $F_4(2^m)$ by spectrum”, Sibirsk. Mat. Zh., 45:6 (2004), 1256–1262; Siberian Math. J., 45:6 (2004), 1031–1035

Citation in format AMSBIB
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\by A.~V.~Vasil'ev, M.~A.~Grechkoseeva, V.~D.~Mazurov, Kh.~P.~Chao, G.~Yu.~Chen, W.~Shi
\paper Recognition of the finite simple groups $F_4(2^m)$ by spectrum
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\vol 45
\issue 6
\pages 1256--1262
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\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 6
\pages 1031--1035
\crossref{https://doi.org/10.1023/B:SIMJ.0000048917.87625.c7}
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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. A. V. Vasil'ev, “On connection between the structure of a finite group and the properties of Its prime graph”, Siberian Math. J., 46:3 (2005), 396–404  mathnet  crossref  mathscinet  zmath  isi  elib
    2. Chen G.Y., Mazurov V.D., Shi W.J., Vasil'ev A.V., Zhurtov A.Kh., “Recognition of the finite almost simple groups PGL(2)(q) by their spectrum”, Journal of Group Theory, 10:1 (2007), 71–85  crossref  mathscinet  zmath  isi  scopus
    3. A. V. Vasil'ev, A. M. Staroletov, “Recognizability of groups $G_2(q)$ by spectrum”, Algebra and Logic, 52:1 (2013), 1–14  mathnet  crossref  mathscinet  zmath  isi
    4. A. S. Kondrat'ev, “Recognizability of groups $E_7(2)$ and $E_7(3)$ by prime graph”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 139–145  mathnet  crossref  mathscinet  isi  elib
    5. A. V. Vasil'ev, A. M. Staroletov, “Almost recognizability by spectrum of simple exceptional groups of Lie type”, Algebra and Logic, 53:6 (2015), 433–449  mathnet  crossref  mathscinet  isi
    6. M. A. Zvezdina, “Spectra of automorphic extensions of finite simple exceptional groups of Lie type”, Algebra and Logic, 55:5 (2016), 354–366  mathnet  crossref  crossref  isi
    7. Grechkoseeva M.A., Zvezdina M.A., “on Spectra of Automorphic Extensions of Finite Simple Groups F-4(Q) and D-3(4)(Q)”, J. Algebra. Appl., 15:9 (2016), 1650168  crossref  mathscinet  zmath  isi  scopus
    8. Grechkoseeva M.A., Vasil'ev A.V., Zvezdina M.A., “Recognition of Symplectic and Orthogonal Groups of Small Dimensions By Spectrum”, J. Algebra. Appl., 18:12 (2019), 1950230  crossref  mathscinet  zmath  isi  scopus
    9. M. A. Grechkoseeva, M. A. Zvezdina, “O raspoznavaemosti po spektru grupp $L_4(q)$$U_4(q)$”, Sib. matem. zhurn., 61:6 (2020), 1300–1330  mathnet  crossref
    10. Lewis M.L. Mirzajani J. Moghaddamfar A.R. Vasil'ev A.V. Zvezdina M.A., “Simple Groups Whose Gruenberg-Kegel Graph Or Solvable Graph Is Split”, Bull. Malays. Math. Sci. Soc., 43:3 (2020), 2523–2547  crossref  mathscinet  zmath  isi  scopus
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