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Algebra Logika, 2002, Volume 41, Number 6, Pages 713–729 (Mi al203)  

Partial Orders of the Group $\mathrm{Aut}\mathbf Q$

A. V. Zenkov


Abstract: We study maximal and minimal partial orders of the group $\mathrm{Aut}\mathbf Q$ of all order automorphisms of a linearly ordered set $\mathbf Q$ of rational numbers. A proof is given for the fact that $\mathrm{Aut}\mathbf Q$ has 36 distinct minimal non-trivial partial orders, and their complete description is provided in. Also, all maximal partial orders of each of the normal subgroups of $\mathrm{Aut}\mathbf Q$ are described.

Keywords: linearly ordered set of rational numbers, maximal partial order, minimal partial order, order automorphism

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English version:
Algebra and Logic, 2002, 41:6, 391–399

Bibliographic databases:

UDC: 512.545
Received: 12.12.2000
Revised: 30.10.2002

Citation: A. V. Zenkov, “Partial Orders of the Group $\mathrm{Aut}\mathbf Q$”, Algebra Logika, 41:6 (2002), 713–729; Algebra and Logic, 41:6 (2002), 391–399

Citation in format AMSBIB
\Bibitem{Zen02}
\by A.~V.~Zenkov
\paper Partial Orders of the Group $\mathrm{Aut}\mathbf Q$
\jour Algebra Logika
\yr 2002
\vol 41
\issue 6
\pages 713--729
\mathnet{http://mi.mathnet.ru/al203}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1967771}
\zmath{https://zbmath.org/?q=an:1031.20002}
\transl
\jour Algebra and Logic
\yr 2002
\vol 41
\issue 6
\pages 391--399
\crossref{https://doi.org/10.1023/A:1021755613605}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42249088903}


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