Geodesic
Partial Orders of the Group $\mathrm{Aut}\mathbf Q$
Algebra i logika, Tome 41 (2002) no. 6, pp. 713-729.

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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, minimal partial order, order automorphism.
Mots-clés : maximal partial order 
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A. V. Zenkov. Partial Orders of the Group $\mathrm{Aut}\mathbf Q$. Algebra i logika, Tome 41 (2002) no. 6, pp. 713-729. http://geodesic.mathdoc.fr/item/AL_2002_41_6_a2/

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