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Algebra Logika, 2014, Volume 53, Number 6, Pages 669–692 (Mi al659)  

This article is cited in 5 scientific papers (total in 5 papers)

Almost recognizability by spectrum of simple exceptional groups of Lie type

A. V. Vasil'evab, A. M. Staroletovba

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: The spectrum of a finite group is the set of its elements orders. Groups are said to be isospectral if their spectra coincide. For every finite simple exceptional group $L=E_7(q)$, we prove that each finite group isospectral to $L$ is isomorphic to a group $G$ squeezed between $L$ and its automorphism group, i.e., $L\le G\le\mathrm{Aut} L$; in particular, up to isomorphism, there are only finitely many such groups. This assertion, together with a series of previously obtained results, implies that the same is true for every finite simple exceptional group except the group $^3D_4(2)$.

Keywords: finite simple groups, exceptional groups of Lie type, element orders, prime graph, recognition by spectrum.

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English version:
Algebra and Logic, 2015, 53:6, 433–449

Bibliographic databases:

UDC: 512.542
Received: 27.09.2014

Citation: A. V. Vasil'ev, A. M. Staroletov, “Almost recognizability by spectrum of simple exceptional groups of Lie type”, Algebra Logika, 53:6 (2014), 669–692; Algebra and Logic, 53:6 (2015), 433–449

Citation in format AMSBIB
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\paper Almost recognizability by spectrum of simple exceptional groups of Lie type
\jour Algebra Logika
\yr 2014
\vol 53
\issue 6
\pages 669--692
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3408302}
\transl
\jour Algebra and Logic
\yr 2015
\vol 53
\issue 6
\pages 433--449
\crossref{https://doi.org/10.1007/s10469-015-9305-1}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. A. Grechkoseeva, A. V. Vasil'ev, “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
    2. 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
    3. Yu. V. Lytkin, “On finite groups isospectral to $U_3(3)$”, Siberian Math. J., 58:4 (2017), 633–643  mathnet  crossref  crossref  isi  elib  elib
    4. Yu. V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584  mathnet  crossref
    5. M. A. Grechkoseeva, “On spectra of almost simple extensions of even-dimensional orthogonal groups”, Siberian Math. J., 59:4 (2018), 623–640  mathnet  crossref  crossref  isi  elib
  • Алгебра и логика Algebra and Logic
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