Algebra i logika
General information
Latest issue
Impact factor

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Algebra Logika:

Personal entry:
Save password
Forgotten password?

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

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

Full text: PDF file (780 kB)
References: PDF file   HTML file

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
\by A.~V.~Vasil'ev, A.~M.~Staroletov
\paper Almost recognizability by spectrum of simple exceptional groups of Lie type
\jour Algebra Logika
\yr 2014
\vol 53
\issue 6
\pages 669--692
\jour Algebra and Logic
\yr 2015
\vol 53
\issue 6
\pages 433--449

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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, 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. Yuri 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
    6. Yuri V. Lytkin, “On finite groups isospectral to the simple group $S_4(3)$”, Sib. elektron. matem. izv., 16 (2019), 1561–1566  mathnet  crossref
    7. M. A. Grechkoseeva, A. V. Vasil'ev, M. A. Zvezdina, “Recognition of symplectic and orthogonal groups of small dimensions by spectrum”, J. Algebra. Appl., 18:12 (2019), 1950230  crossref  mathscinet  zmath  isi  scopus
    8. Yang N. Grechkoseeva M.A. Vasil'ev A.V., “on the Nilpotency of the Solvable Radical of a Finite Group Isospectral to a Simple Group”, J. Group Theory, 23:3 (2020), 447–470  crossref  mathscinet  zmath  isi  scopus
    9. A. M. Staroletov, “O kompozitsionnykh faktorakh konechnykh grupp, izospektralnykh prostym klassicheskim gruppam”, Sib. matem. zhurn., 62:2 (2021), 422–440  mathnet  crossref
  • Алгебра и логика Algebra and Logic
    Number of views:
    This page:353
    Full text:76
    First page:18

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021