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Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 4, Pages 155–166 (Mi timm1009)  

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

On nonabelian composition factors of a finite group that is prime spectrum minimal

N. V. Maslovaab, D. O. Revincd

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
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
d Novosibirsk State University

Abstract: Suppose that $L$ is a finite group, $\pi(L)$ is the set of prime divisors of the order $|L|$, and $\mathfrak{Y}$ is the class of finite groups $G$ such that $\pi(G) \not = \pi(H)$ for any proper subgroup $H$ of $G$. Groups from the class $\mathfrak{Y}$ will be called prime spectrum minimal. Many but not all finite simple groups are prime spectrum minimal. For finite simple groups not from the class $\mathfrak{Y}$, the question whether they are isomorphic to nonabelian composition factors of groups from the class $\mathfrak{Y}$ is interesting. We describe some finite simple groups that are not isomorphic to nonabelian composition factors of groups from the class $\mathfrak{Y}$ and construct an example of a finite group from $\mathfrak{Y}$ that has as its composition factor a finite simple sporadic McLaughlin group $McL$ not from the class $\mathfrak{Y}$.

Keywords: finite group, prime spectrum, minimal group, maximal subgroup, composition factor.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, 287, suppl. 1, 116–127

Bibliographic databases:

Document Type: Article
UDC: 512.542
Received: 25.03.2013

Citation: N. V. Maslova, D. O. Revin, “On nonabelian composition factors of a finite group that is prime spectrum minimal”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 155–166; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 116–127

Citation in format AMSBIB
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\paper On nonabelian composition factors of a finite group that is prime spectrum minimal
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\vol 19
\issue 4
\pages 155--166
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2014
\vol 287
\issue , suppl. 1
\pages 116--127
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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. 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, “On the finite prime spectrum minimal groups”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 109–119  mathnet  crossref  mathscinet  elib
    4. W. Guo, D. O. Revin, “Maximal and submaximal $\mathfrak X$-subgroups”, Algebra and Logic, 57:1 (2018), 9–28  mathnet  crossref  crossref  isi
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