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Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 1, Pages 172–176 (Mi timm1153)  

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

Finite simple groups that are not spectrum critical

N. V. Maslovaab

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

Abstract: Let $G$ be a finite group. The spectrum of $G$ is the set $\omega(G)$ of orders of all its elements. The subset of prime elements of $\omega(G)$ is called prime spectrum and is denoted by $\pi(G)$. A group $G$ is called spectrum critical ( prime spectrum critical) if, for any subgroups $K$ and $L$ of $G$ such that $K$ is a normal subgroup of $L$, the equality $\omega(L/K)=\omega(G)$ ($\pi(L/K)=\pi(G)$, respectively) implies that $L=G$ and $K=1$. In the present paper, we describe all finite simple groups that are not spectrum critical. In addition, we show that a prime spectrum minimal group $G$ is prime spectrum critical if and only if its Fitting subgroup $F(G)$ is a Hall subgroup of $G$.

Keywords: finite group; simple group; spectrum; prime spectrum; spectrum critical group; prime spectrum critical group.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, 292, suppl. 1, 211–215

Bibliographic databases:

UDC: 512.542
Received: 30.07.2014

Citation: N. V. Maslova, “Finite simple groups that are not spectrum critical”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 1, 2015, 172–176; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 211–215

Citation in format AMSBIB
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\paper Finite simple groups that are not spectrum critical
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 1
\pages 172--176
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\vol 292
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\pages 211--215
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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 groups with arithmetic restrictions on maximal subgroups”, Algebra and Logic, 54:1 (2015), 65–69  mathnet  crossref  crossref  mathscinet  isi
    2. A. Pachera, “Exponent preserving subgroups of the finite simple groups”, Commun. Algebr., 45:6 (2017), 2494–2504  crossref  mathscinet  zmath  isi  scopus
    3. Yuri V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584  mathnet  crossref
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