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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 3, Pages 29–44 (Mi timm961)  

This article is cited in 5 scientific papers (total in 5 papers)

On control of the prime spectrum of the finite simple groups

V. A. Belonogov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (250 kB) Citations (5)
References:
Abstract: The set $\pi(G)$ of all prime divisors of the order of a finite group $G$ is often called its prime spectrum. It is proved that every finite simple nonabelian group $G$ has sections $H_1,\dots,H_m$ of some special form such that $\pi(H_1)\cup\dots\cup\pi(H_m)=\pi(G)$ and $m\le5$, in the case when $G$ is an alternating or classical simple group, in addition, $m\le2$. Moreover, in any case, it is possible to choose the sections $H_i$ so that each of them is a simple nonabelian group, a Frobenius group, or (in one case) a dihedral group. If the above equality is realized for a finite group $G$, then we say that the set $\{H_1,\dots,H_m\}$ controls the prime spectrum of $G$. We also study some parameter $c(G)$ of finite groups $G$ related to the notion of control.
Keywords: finite group, simple group, prime spectrum, maximal subgroup, section of a group.
Received: 20.08.2012
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 285, Issue 1, Pages S25–S4110
DOI: https://doi.org/10.1134/S0081543814050046
Bibliographic databases:
Document Type: Article
UDC: 512.54
Language: Russian
Citation: V. A. Belonogov, “On control of the prime spectrum of the finite simple groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 3, 2013, 29–44; Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S25–S4110
Citation in format AMSBIB
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\by V.~A.~Belonogov
\paper On control of the prime spectrum of the finite simple groups
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\yr 2013
\vol 19
\issue 3
\pages 29--44
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2014
\vol 285
\issue , suppl. 1
\pages S25--S4110
\crossref{https://doi.org/10.1134/S0081543814050046}
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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