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Algebra Logika, 2013, Volume 52, Number 1, Pages 3–21 (Mi al568)  

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

Recognizability of groups $G_2(q)$ by spectrum

A. V. Vasil'evab, A. M. Staroletova

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: Two groups are said to be isospectral if they have equal sets of element orders. It is proved that for every finite simple exceptional group $L=G_2(q)$ of Lie type, any finite group $G$ isospectral to $L$ must be isomorphic to $L$.

Keywords: finite simple group, exceptional group of Lie type, element order, spectrum of group, recognition by spectrum.

Full text: PDF file (273 kB)
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English version:
Algebra and Logic, 2013, 52:1, 1–14

Bibliographic databases:

UDC: 512.542
Received: 13.11.2012
Revised: 29.12.2012

Citation: A. V. Vasil'ev, A. M. Staroletov, “Recognizability of groups $G_2(q)$ by spectrum”, Algebra Logika, 52:1 (2013), 3–21; Algebra and Logic, 52:1 (2013), 1–14

Citation in format AMSBIB
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\paper Recognizability of groups $G_2(q)$ by spectrum
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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. M. A. Grechkoseeva, “Element orders in covers of finite simple groups”, Algebra and Logic, 52:5 (2013), 426–428  mathnet  crossref  mathscinet  isi
    2. 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
    3. 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
    4. Grechkoseeva M.A., “Element Orders in Covers of Finite Simple Groups of Lie Type”, J. Algebra. Appl., 14:4 (2015), 1550056  crossref  mathscinet  zmath  isi  elib  scopus
    5. A. A. Buturlakin, “Spectra of the finite simple groups $E_7(q)$”, Siberian Math. J., 57:5 (2016), 769–777  mathnet  crossref  crossref  isi  elib  elib
    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. M. A. Grechkoseeva, M. A. Zvezdina, “On spectra of automorphic extensions of finite simple groups $F_4(q)$ and $^3D_4(q)$”, J. Algebra. Appl., 15:9 (2016), 1650168  crossref  mathscinet  zmath  isi  scopus
    8. Yu. V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584  mathnet  crossref
    9. A. A. Buturlakin, “Spectra of groups $E_8(q)$”, Algebra and Logic, 57:1 (2018), 1–8  mathnet  crossref  crossref  isi
    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  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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