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

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.

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

Bibliographic databases:

UDC: 519.44

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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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
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