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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 683–689
DOI: https://doi.org/10.33048/semi.2020.17.046
(Mi semr1241)
 

This article is cited in 2 scientific papers (total in 2 papers)

Mathematical logic, algebra and number theory

Factoring nonabelian finite groups into two subsets

R. R. Bildanova, V. A. Goryachenkob, A. V. Vasil'evc

a Specialized Educational Scientific Center of Novosibirsk State University, 11/1, Pirogova str., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
c Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
Full-text PDF (357 kB) Citations (2)
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Abstract: A group $G$ is said to be factorized into subsets $A_1, A_2,$ $\ldots, A_s\subseteq G$ if every element $g$ in $G$ can be uniquely represented as $g=g_1g_2\ldots g_s$, where $g_i\in A_i$, $i=1,2,\ldots,s$. We consider the following conjecture: for every finite group $G$ and every factorization $n=ab$ of its order, there is a factorization $G=AB$ with $|A|=a$ and $|B|=b$. We show that a minimal counterexample to this conjecture must be a nonabelian simple group and prove the conjecture for every finite group the nonabelian composition factors of which have orders less than $10 000$.
Keywords: factoring of groups into subsets, finite group, finite simple group, maximal subgroups.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences 0314-2019-0001
The third author was supported by the program of fundamental scientific researches of the Russian Federation, Project 0314-2019-0001.
Received April 30, 2020, published May 21, 2020
Bibliographic databases:
Document Type: Article
UDC: 512.542
MSC: 20D60
Language: English
Citation: R. R. Bildanov, V. A. Goryachenko, A. V. Vasil'ev, “Factoring nonabelian finite groups into two subsets”, Sib. Èlektron. Mat. Izv., 17 (2020), 683–689
Citation in format AMSBIB
\Bibitem{BilGorVas20}
\by R.~R.~Bildanov, V.~A.~Goryachenko, A.~V.~Vasil'ev
\paper Factoring nonabelian finite groups into two subsets
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 683--689
\mathnet{http://mi.mathnet.ru/semr1241}
\crossref{https://doi.org/10.33048/semi.2020.17.046}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000537772100001}
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  • https://www.mathnet.ru/eng/semr/v17/p683
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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