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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 1, Pages 156–168 (Mi timm1039)  

This article is cited in 4 scientific papers (total in 4 papers)

On the coincidence of Grünberg–Kegel graphs of a finite simple group and its proper subgroup

N. V. Maslovaab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University named after the First President of Russia B. N. Yeltsin

Abstract: Let $G$ be a finite group. The spectrum of $G$ is the set $\omega(G)$ of orders of its elements. The subset of prime elements of $\omega(G)$ is denoted by $\pi(G)$. The spectrum $\omega(G)$ of a group $G$ defines its prime graph (or Grünberg–Kegel graph) $\Gamma(G)$ with vertex set $\pi(G)$, in which any two different vertices $r$ and $s$ are adjacent if and only if the number $rs$ belongs to the set $\omega(G)$. We describe all the cases when the prime graphs of a finite simple group and of its proper subgroup coincide.

Keywords: finite group, simple group, prime spectrum, prime graph (Grünberg–Kegel graph), maximal subgroup.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 288, suppl. 1, 129–141

Bibliographic databases:

Document Type: Article
UDC: 512.542
Received: 06.11.2013

Citation: N. V. Maslova, “On the coincidence of Grünberg–Kegel graphs of a finite simple group and its proper subgroup”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 156–168; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 129–141

Citation in format AMSBIB
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\paper On the coincidence of Gr\"unberg--Kegel graphs of a~finite simple group and its proper subgroup
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\vol 20
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\pages 156--168
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\pages 129--141
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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. 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
    2. N. V. Maslova, “Finite groups with arithmetic restrictions on maximal subgroups”, Algebra and Logic, 54:1 (2015), 65–69  mathnet  crossref  crossref  mathscinet  isi
    3. N. V. Maslova, D. Pagon, “On the realizability of a graph as the Gruenberg–Kegel graph of a finite group”, Sib. elektron. matem. izv., 13 (2016), 89–100  mathnet  crossref
    4. I. B. Gorshkov, N. V. Maslova, “Finite almost simple groups whose Gruenberg–Kegel graphs coincide with Gruenberg–Kegel graphs of solvable groups”, Algebra and Logic, 57:2 (2018), 115–129  mathnet  crossref  crossref  isi
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