Unilateral \(o\)-groups. (Russian, English) Zbl 1115.06008

Glass, A. M. W.; Medvedev, N. Ya.

Algebra Logika 45, No. 1, 20-27 (2006); translation in Algebra Logic 45, No. 1, 12-16 (2006).

Summary: For a big number of varieties \(\mathcal V\) of groups close to Engelian, it is proved that a variety of lattice-ordered groups generated by all linearly ordered groups in the class \(\mathcal P\mathcal V = \bigcup\limits_{k\in\mathbb Z_+}\mathcal V^k\) does not coincide with the variety \(\mathcal O_l\) of all \(o\)-approximable lattice-ordered groups.

MSC:

06F15	Ordered groups
20D10	Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20F16	Solvable groups, supersolvable groups
20F60	Ordered groups (group-theoretic aspects)

Keywords:

unilateral \(o\)-group; Engelian group; lattice-ordered group