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.

UDC: 512.545

Received: 12.12.2000
Revised: 30.10.2002

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

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