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Mat. Zametki, 1976, Volume 19, Issue 1, Pages 85–90 (Mi mz7725)  

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

Linearly ordered groups whose system of convex subgroups is central

V. M. Kopytov, N. Ya. Medvedev

Novosibirsk State University

Abstract: The order $P$ on a group $G$ is called rigid if for $p\in P$ the relation $p|[x,p]|^\varepsilon\in P$ holds for every $x\in G$, $\varepsilon=\pm1$ In this note we give criteria for the existence of a rigid linear order, for the extendability of a rigid partial order to a rigid linear order, and for the extendability of each rigid partial order to a rigid linear order on a group. It is proved that the class of groups each of whose rigid partial orders can be extended to a rigid linear order is closed with respect to direct products. A new proof of the theorem of M. I. Kargapolov which states that if a group $G$ can be approximated by finite $p$-groups for infinite number of primes $p$, then it has a central system of subgroups with torsion-free factors is presented.

Full text: PDF file (550 kB)

English version:
Mathematical Notes, 1976, 19:1, 49–52

Bibliographic databases:

UDC: 519.44
Received: 08.12.1974

Citation: V. M. Kopytov, N. Ya. Medvedev, “Linearly ordered groups whose system of convex subgroups is central”, Mat. Zametki, 19:1 (1976), 85–90; Math. Notes, 19:1 (1976), 49–52

Citation in format AMSBIB
\Bibitem{KopMed76}
\by V.~M.~Kopytov, N.~Ya.~Medvedev
\paper Linearly ordered groups whose system of convex subgroups is central
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 1
\pages 85--90
\mathnet{http://mi.mathnet.ru/mz7725}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=406903}
\zmath{https://zbmath.org/?q=an:0358.06036}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 1
\pages 49--52
\crossref{https://doi.org/10.1007/BF01147617}


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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. V. M. Kopytov, N. Ya. Medvedev, “Varieties of lattice ordered groups”, Russian Math. Surveys, 40:6 (1985), 97–110  mathnet  crossref  mathscinet  zmath  adsnasa
  • Математические заметки Mathematical Notes
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