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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2017, Issue 3(32), Pages 58–60
(Mi pfmt519)
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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.
Received: 07.06.2017
Citation:
V. S. Monakhov, “The nilpotency criterion for the derived subgroup of a finite group”, PFMT, 2017, no. 3(32), 58–60
Linking options:
https://www.mathnet.ru/eng/pfmt519 https://www.mathnet.ru/eng/pfmt/y2017/i3/p58
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| Statistics & downloads: |
| Abstract page: | 270 | | Full-text PDF : | 66 | | References: | 44 |
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