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Vladikavkaz. Mat. Zh., 2011, Volume 13, Number 4, Pages 35–39 (Mi vmj400)  

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

2-groups with given properties of finite subgroups

D. V. Lytkina

Siberian State University of Telecommunications and Informatics, Novosibirsk, Russia

Abstract: A local finiteness is proved of 2-groups, all of whose finite subgroups (a) are nilpotent of class 2 or (b) belong to a variety defined by the law $[x,y]^2=1$. Besides, it is proved that the order of the derived subgroup of a 2-group $G$ is at most 2 if the order of every conjugacy class of every finite subgroup of $G$ is at most 2.

Key words: periodic group, nilpotency, local finiteness.

Full text: PDF file (115 kB)
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Document Type: Article
UDC: 512.542
Received: 19.05.2011

Citation: D. V. Lytkina, “2-groups with given properties of finite subgroups”, Vladikavkaz. Mat. Zh., 13:4 (2011), 35–39

Citation in format AMSBIB
\Bibitem{Lyt11}
\by D.~V.~Lytkina
\paper 2-groups with given properties of finite subgroups
\jour Vladikavkaz. Mat. Zh.
\yr 2011
\vol 13
\issue 4
\pages 35--39
\mathnet{http://mi.mathnet.ru/vmj400}


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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. D. V. Lytkina, V. D. Mazurov, “Groups with given properties of finite subgroups”, Algebra and Logic, 51:3 (2012), 213–219  mathnet  crossref  mathscinet  zmath  isi
    2. Lytkina D.V., Mazurov V.D., “Nekotorye otkrytye voprosy teorii grupp”, Matematicheskii forum (itogi nauki. yug Rossii), 6 (2012), 98–104  mathscinet  elib
    3. A. A. Shlepkin, “Periodicheskie gruppy, nasyschennye spletennymi gruppami”, Sib. elektron. matem. izv., 10 (2013), 56–64  mathnet
    4. D. V. Lytkina, V. D. Mazurov, “On groups with given properties of the finite subgroups generated by couples of $2$-elements”, Siberian Math. J., 54:1 (2013), 96–98  mathnet  crossref  mathscinet  isi
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