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Algebra Logika, 2016, Volume 55, Number 5, Pages 540–557 (Mi al760)  

This article is cited in 3 scientific papers (total in 3 papers)

Spectra of automorphic extensions of finite simple exceptional groups of Lie type

M. A. Zvezdinaab

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 $\omega(G)$ of a finite group $G$ is the set of orders of elements of $G$. Let $S$ be a simple exceptional group of type $E_6$ or $E_7$. We describe all finite groups $G$ such that $S\le G\le\operatorname{Aut}S$ and $\omega(G)=\omega(S)$. Along with the previously obtained results, this provides a description of all finite groups $G$ such that $\omega(G)=\omega(S)$ and completes the study of the recognition-by-spectrum problem for all simple exceptional groups of Lie type.

Keywords: automorphic extension, exceptional group, finite simple group, order of element, recognizability by spectrum.

Funding Agency Grant Number
Russian Science Foundation 14-21-00065
Supported by Russian Science Foundation, project 14-21-00065.


DOI: https://doi.org/10.17377/alglog.2016.55.502

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English version:
Algebra and Logic, 2016, 55:5, 354–366

Bibliographic databases:

Document Type: Article
UDC: 512.542
Received: 11.12.2015

Citation: M. A. Zvezdina, “Spectra of automorphic extensions of finite simple exceptional groups of Lie type”, Algebra Logika, 55:5 (2016), 540–557; Algebra and Logic, 55:5 (2016), 354–366

Citation in format AMSBIB
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\by M.~A.~Zvezdina
\paper Spectra of automorphic extensions of finite simple exceptional groups of Lie type
\jour Algebra Logika
\yr 2016
\vol 55
\issue 5
\pages 540--557
\mathnet{http://mi.mathnet.ru/al760}
\crossref{https://doi.org/10.17377/alglog.2016.55.502}
\transl
\jour Algebra and Logic
\yr 2016
\vol 55
\issue 5
\pages 354--366
\crossref{https://doi.org/10.1007/s10469-016-9407-4}
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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, “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
    2. M. A. Grechkoseeva, “Orders of elements of finite almost simple groups”, Algebra and Logic, 56:6 (2018), 502–505  mathnet  crossref  crossref  isi
    3. 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
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