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Groups of formal power series are fully orderable. (English. Russian original) Zbl 0905.20028
Algebra Logika 37, No. 3, 301-319 (1998); translation in Algebra Logic 37, No. 3, 170-180 (1998).
The examples of fully orderable groups known by now were obtained using direct products and the local theorem for torsion-free nilpotent groups and ordered solvable groups of derived length 2. There are also some isolated examples of fully orderable groups each of which is likewise solvable. Yet, there are no examples of fully orderable groups that are not locally solvable (at least they are missing in the literature). The author constructs an example of a fully orderable group that is not locally solvable. The group admits a weakly Abelian linear order, i.e., it contains a central series of subgroups with torsion-free factors. The author also shows that a free group is embedded in a fully orderable group. To this end, use is made of a group of invertible formal power series with zero free term under composition.

MSC:
20F60 Ordered groups (group-theoretic aspects)
06F15 Ordered groups
20F19 Generalizations of solvable and nilpotent groups
20E07 Subgroup theorems; subgroup growth
20F14 Derived series, central series, and generalizations for groups
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