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PFMT, 2017, Issue 3(32), Pages 58–60 (Mi pfmt519)  

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

MATHEMATICS

The nilpotency criterion for the derived subgroup of a finite group

V. S. Monakhov

F. Scorina Gomel State University

Abstract: It is proved that the derived subgroup of a finite group is nilpotent if and only if $|ab|\geqslant |a||b|$ for all primary commutators $a$ and $b$ of coprime orders.

Keywords: finite group, commutator, derived subgroup, nilpotent subgroup.

Full text: PDF file (300 kB)
References: PDF file   HTML file
UDC: 512.542
Received: 07.06.2017
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Citation: V. S. Monakhov, “The nilpotency criterion for the derived subgroup of a finite group”, PFMT, 2017, no. 3(32), 58–60

Citation in format AMSBIB
\Bibitem{Mon17}
\by V.~S.~Monakhov
\paper The nilpotency criterion for the derived subgroup of a finite group
\jour PFMT
\yr 2017
\issue 3(32)
\pages 58--60
\mathnet{http://mi.mathnet.ru/pfmt519}


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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. V. S. Monakhov, “A metanilpotency criterion for a finite solvable group”, Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S141–S143  mathnet  crossref  crossref  isi  elib
    2. R. Bastos, C. Monetta, “Coprime commutators in finite groups”, Communications in Algebra, 47:10 (2019), 4137–4147  crossref  mathscinet  zmath  scopus
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