Sentence examples for orderable group from inspiring English sources

The question if there exists a finitely generated, totally orderable group of intermediate growth is still open.

The paper [13] also contains an example of a torsion free group of intermediate growth, which happened to be right orderable group, as was shown in [19].

Every right orderable group is left orderable and vise versa but there are right orderable groups which are not totally orderable (see [26] for examples).

(i) Let (G) be a finitely generated right orderable group with growth (prec e^{n^{1/6}}.) In [32] Morris proved that every finitely generated right orderable amenable group is indicable (i.e. can be mapped onto (mathbb Z )).

In a similar way are defined left orderable groups.

The cases of residually solvable groups and right orderable groups are considered as well.

(i) The Gap Conjecture with parameter (1/6,) and, moreover, the conjecture (C^*(1/6)) hold for right orderable groups.

The Gap Conjecture and it modifications stated in Sect. 3 are interesting problems even for the class of right orderable groups.

As was shown by Machi and the author the class of finitely generated right orderable groups of intermediate growth is nonempty [19].

(ii) The Gap Conjecture (C(1/2)) [or its -version (C^*(1/2))] holds for right orderable groups if it [or its -version (C^*(1/2))] holds for residually polycyclic groups.

It was implicitly observed in [19] that the class of countable right orderable groups coincides with the class of groups acting faithfully by homeomorphisms on the line (mathbb R ) (or, what is the same, on the interval ([0,1])).