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Sib. Èlektron. Mat. Izv., 2011, Volume 8, Pages 369–371 (Mi semr335)  

This article is cited in 1 scientific paper (total in 1 paper)

Partial generalization of one of Macdonald's results

D. V. Lytkina

Siberian State University of Telecommunications and Informatics

Abstract: It is proved that if in every finite subgroup of a $2$-group $G$ the identity $[x,y]^2=1$ holds, then this identity holds in $G$ also. In particular, $G$ is locally finite, its derived subgroup is of exponent 4, and the second derived subgroup belongs to the center of $G$.

Keywords: $p$-группа, коммутант.

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Document Type: Article
UDC: 512.5
MSC: 20D15
Received September 9, 2011, published December 20, 2011

Citation: D. V. Lytkina, “Partial generalization of one of Macdonald's results”, Sib. Èlektron. Mat. Izv., 8 (2011), 369–371

Citation in format AMSBIB
\Bibitem{Lyt11}
\by D.~V.~Lytkina
\paper Partial generalization of one of Macdonald's results
\jour Sib. \`Elektron. Mat. Izv.
\yr 2011
\vol 8
\pages 369--371
\mathnet{http://mi.mathnet.ru/semr335}


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    This publication is cited in the following articles:
    1. A. A. Shlepkin, “Periodicheskie gruppy, nasyschennye spletennymi gruppami”, Sib. elektron. matem. izv., 10 (2013), 56–64  mathnet
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