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Algebra Logika, 2005, Volume 44, Number 5, Pages 517–539 (Mi al129)  

This article is cited in 9 scientific papers (total in 9 papers)

Quasirecognizability by the Set of Element Orders for Groups $^3D_4(q)$ and $F_4(q)$, for $q$ Odd

O. A. Alekseevaa, A. S. Kondrat'evb

a Chelyabinsk Institute of Humanities
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: It is proved that if $L$ is one of the simple groups $^3D_4(q)$ or $F_4(q)$, where $q$ is odd, and $G$ is a finite group with the set of element orders as in $L$, then the derived subgroup of $G/F(G)$ is isomorphic to $L$ and the factor group $G/G'$ is a cyclic $\{2,3\}$-group.

Keywords: finite group, simple group, set of element orders, quasirecognizability, prime graph

Full text: PDF file (277 kB)
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English version:
Algebra and Logic, 2005, 44:5, 287–301

Bibliographic databases:

UDC: 512.542
Received: 06.12.2004

Citation: O. A. Alekseeva, A. S. Kondrat'ev, “Quasirecognizability by the Set of Element Orders for Groups $^3D_4(q)$ and $F_4(q)$, for $q$ Odd”, Algebra Logika, 44:5 (2005), 517–539; Algebra and Logic, 44:5 (2005), 287–301

Citation in format AMSBIB
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\by O.~A.~Alekseeva, A.~S.~Kondrat'ev
\paper Quasirecognizability by the Set of Element Orders for Groups~$^3D_4(q)$ and~$F_4(q)$, for $q$~Odd
\jour Algebra Logika
\yr 2005
\vol 44
\issue 5
\pages 517--539
\mathnet{http://mi.mathnet.ru/al129}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2195018}
\zmath{https://zbmath.org/?q=an:1104.20019}
\elib{http://elibrary.ru/item.asp?id=9027754}
\transl
\jour Algebra and Logic
\yr 2005
\vol 44
\issue 5
\pages 287--301
\crossref{https://doi.org/10.1007/s10469-005-0028-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-27544496157}


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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. O. A. Alekseeva, “Quasirecognizability by the Set of Element Orders for Groups ${^3}D_4(q)$, for $q$ Even”, Algebra and Logic, 45:1 (2006), 1–11  mathnet  crossref  mathscinet  zmath  elib  elib
    2. A. S. Kondrat'ev, “Quasirecognition by the set of element orders of the groups $E_6(q)$ and $^2E_6(q)$”, Siberian Math. J., 48:6 (2007), 1001–1018  mathnet  crossref  mathscinet  zmath  isi  elib
    3. O. A. Alekseeva, A. S. Kondratev, “Raspoznavaemost po spektru grupp $ ^2D_p(3)$ dlya nechetnogo prostogo chisla $p$”, Tr. IMM UrO RAN, 14, no. 4, 2008, 3–11  mathnet  elib
    4. Darafsheh M.R., Karamzadeh N.S., “On recognition property of some projective special linear groups by their element orders”, Utilitas Mathematica, 75 (2008), 125–137  mathscinet  zmath  isi  elib
    5. O. A. Alekseeva, A. S. Kondrat'ev, “On recognizability of some finite simple orthogonal groups by spectrum”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S10–S23  mathnet  crossref  isi  elib
    6. Kondrat'ev A.S., “Recognition by spectrum of the groups $^2D_{2^m+1}(3)$”, Sci. China Ser. A, 52:2 (2009), 293–300  crossref  mathscinet  zmath  isi  scopus
    7. A. S. Kondratev, “O raspoznavaemosti po spektru konechnykh prostykh ortogonalnykh grupp, II”, Vladikavk. matem. zhurn., 11:4 (2009), 32–43  mathnet  elib
    8. 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
    9. 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
  • Алгебра и логика Algebra and Logic
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