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Algebra Logika, 2006, Volume 45, Number 2, Pages 185–202 (Mi al141)  

This article is cited in 26 scientific papers (total in 26 papers)

Recognition of Simple Groups $U_3(Q)$ by Element Orders

A. V. Zavarnitsin

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

Abstract: An exhaustive solution is given to the recognition-by-spectrum problem for finite, simple, three-dimensional unitary groups. For every such group, the number of non-isomorphic, finite, isospectral groups is determined. In particular, a new counterexample to Problem 13.63 in the Kourovka Notebook is furnished.

Keywords: finite group, element order, recognition, spectrum

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English version:
Algebra and Logic, 2006, 45:2, 106–116

Bibliographic databases:

UDC: 512.542
Received: 05.01.2005

Citation: A. V. Zavarnitsin, “Recognition of Simple Groups $U_3(Q)$ by Element Orders”, Algebra Logika, 45:2 (2006), 185–202; Algebra and Logic, 45:2 (2006), 106–116

Citation in format AMSBIB
\by A.~V.~Zavarnitsin
\paper Recognition of Simple Groups $U_3(Q)$ by Element Orders
\jour Algebra Logika
\yr 2006
\vol 45
\issue 2
\pages 185--202
\jour Algebra and Logic
\yr 2006
\vol 45
\issue 2
\pages 106--116

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    This publication is cited in the following articles:
    1. V. D. Mazurov, G. Y. Chen, “Recognizability of finite simple groups $L_4(2^m)$ and $U_4(2^m)$ by spectrum”, Algebra and Logic, 47:1 (2008), 49–55  mathnet  crossref  mathscinet  zmath  isi
    2. M. A. Grechkoseeva, “Recognition by spectrum for finite linear groups over fields of characteristic 2”, Algebra and Logic, 47:4 (2008), 229–241  mathnet  crossref  mathscinet  zmath  isi
    3. Grechkoseeva M.A., Shi W., Vasilev A.V., “Recognition by spectrum for finite simple groups of Lie type”, Front. Math. China, 3:2 (2008), 275–285  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. D. Mazurov, “O raspoznavanii konechnykh prostykh grupp po spektru”, Tr. In-ta matem., 16:1 (2008), 59–63  mathnet
    5. A. V. Zavarnitsine, “Exceptional action of the simple groups $L_4(q)$ in the defining characteristic”, Sib. elektron. matem. izv., 5 (2008), 68–74  mathnet  mathscinet
    6. Xu Mingchun, “Recognition of finite simple linear groups $L_4(2^k)$ by spectrum”, Algebra Colloq., 17:3 (2010), 469–474  crossref  mathscinet  zmath  isi  scopus
    7. A. V. Vasil'ev, M. A. Grechkoseeva, A. M. Staroletov, “On finite groups isospectral to simple linear and unitary groups”, Siberian Math. J., 52:1 (2011), 30–40  mathnet  crossref  mathscinet  isi
    8. A. M. Staroletov, “Sporadic composition factors of finite groups isospectral to simple groups”, Sib. elektron. matem. izv., 8 (2011), 268–272  mathnet
    9. M. A. Grechkoseeva, D. V. Lytkin, “Almost recognizability by spectrum of finite simple linear groups of prime dimension”, Siberian Math. J., 53:4 (2012), 645–655  mathnet  crossref  mathscinet  isi
    10. M. A. Grechkoseeva, W. J. Shi, “On finite groups isospectral to finite simple unitary groups over fields of characteristic 2”, Sib. elektron. matem. izv., 10 (2013), 31–37  mathnet
    11. M. A. Zvezdina, “Spectra of automorphic extensions of finite simple symplectic and orthogonal groups over fields of characteristic 2”, Sib. elektron. matem. izv., 11 (2014), 823–832  mathnet
    12. N. V. Maslova, “Finite simple groups that are not spectrum critical”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 211–215  mathnet  crossref  mathscinet  isi  elib
    13. Grechkoseeva M.A. Vasil'ev A.V., “on the Structure of Finite Groups Isospectral To Finite Simple Groups”, J. Group Theory, 18:5 (2015), 741–759  crossref  mathscinet  zmath  isi  elib  scopus
    14. 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
    15. Vasil'ev A.V., “on Finite Groups Isospectral to Simple Classical Groups”, J. Algebra, 423 (2015), 318–374  crossref  mathscinet  zmath  isi  scopus
    16. M. A. Grechkoseeva, “On spectra of almost simple groups with symplectic or orthogonal socle”, Siberian Math. J., 57:4 (2016), 582–588  mathnet  crossref  crossref  isi  elib  elib
    17. 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
    18. 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
    19. Grechkoseeva M.A., “On Orders of Elements of Finite Almost Simple Groups With Linear Or Unitary Socle”, J. Group Theory, 20:6 (2017), 1191–1222  crossref  mathscinet  zmath  isi  scopus
    20. M. A. Grechkoseeva, “Orders of elements of finite almost simple groups”, Algebra and Logic, 56:6 (2018), 502–505  mathnet  crossref  crossref  isi
    21. Yuri V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584  mathnet  crossref
    22. Mahmoudifar A., “on a Conjecture About the Quasirecognition By Prime Graph of Some Finite Simple Groups”, J. Algebra. Appl., 18:4 (2019), 1950070  crossref  mathscinet  zmath  isi  scopus
    23. M. A. Grechkoseeva, S. V. Skresanov, “On element orders in covers of $L_4(q)$ and $U_4(q)$”, Sib. elektron. matem. izv., 17 (2020), 585–589  mathnet  crossref
    24. M. Akbari, X. Y. Chen, A. R. Moghaddamfar, “An OD-characterizable class of simple groups”, Algebra Discrete Math., 29:1 (2020), 42–51  mathnet  crossref
    25. Di Martino L., Pellegrini M.A., Zalesski A.E., “Almost Cyclic Elements in Cross-Characteristic Representations of Finite Groups of Lie Type”, J. Group Theory, 23:2 (2020), 235–285  crossref  mathscinet  zmath  isi  scopus
    26. Akbari M. Chen X. Moghaddamfar A., “Od-Characterization of Some Simple Unitary Groups”, Bull. Iran Math. Soc., 47:1 (2021), 197–215  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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