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Algebra Logika, 2002, Volume 41, Number 2, Pages 130–142 (Mi al176)  

This article is cited in 12 scientific papers (total in 12 papers)

Recognizing Groups $G_2(3^n)$ by Their Element Orders

A. V. Vasil'ev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: It is proved that a finite group that is isomorphic to a simple non-Abelian group $G=G_2(3^n)$ is, up to isomorphism, recognized by a set $\omega(G)$ of its element orders, that is, $H \simeq G$ if $\omega(H)=\omega(G)$ for some finite group $H$.

Keywords: finite group, simple non-Abelian group, recognizability of groups by their element orders

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English version:
Algebra and Logic, 2002, 41:2, 74–80

Bibliographic databases:

UDC: 512.542
Received: 31.07.2000

Citation: A. V. Vasil'ev, “Recognizing Groups $G_2(3^n)$ by Their Element Orders”, Algebra Logika, 41:2 (2002), 130–142; Algebra and Logic, 41:2 (2002), 74–80

Citation in format AMSBIB
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\transl
\jour Algebra and Logic
\yr 2002
\vol 41
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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. D. Mazurov, “Recognition of Finite Simple Groups $S_4(q)$ by Their Element Orders”, Algebra and Logic, 41:2 (2002), 93–110  mathnet  crossref  mathscinet  zmath
    2. M. A. Grechkoseeva, “Recognition of the group $O_{10}^+(2)$ from its spectrum”, Siberian Math. J., 44:4 (2003), 577–580  mathnet  crossref  mathscinet  zmath  isi
    3. 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”, Siberian Math. J., 45:6 (2004), 1031–1035  mathnet  crossref  mathscinet  zmath  isi  elib
    4. Zavarnitsine AV, “Recognition of the simple groups L-3(q) by element orders”, Journal of Group Theory, 7:1 (2004), 81–97  crossref  mathscinet  zmath  isi
    5. Mazurov V.D., “Characterizations of groups by arithmetic properties”, Algebra Colloquium, 11:1 (2004), 129–140  mathscinet  zmath  isi
    6. M. A. Grechkoseeva, “Quasirecognizability of simple unitary groups over fields of even order”, Sib. elektron. matem. izv., 7 (2010), 435–444  mathnet
    7. A. M. Staroletov, “Sporadic composition factors of finite groups isospectral to simple groups”, Sib. elektron. matem. izv., 8 (2011), 268–272  mathnet
    8. A. M. Staroletov, “On recognition by spectrum of the simple groups $B_3(q)$, $C_3(q)$, and $D_4(q)$”, Siberian Math. J., 53:3 (2012), 532–538  mathnet  crossref  mathscinet  isi
    9. 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
    10. 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
    11. 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
    12. A. V. Vasil'ev, M. A. Grechkoseeva, “Recognition by spectrum for simple classical groups in characteristic $2$”, Siberian Math. J., 56:6 (2015), 1009–1018  mathnet  crossref  crossref  mathscinet  isi  elib
  • Алгебра и логика Algebra and Logic
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