Normal relatively convex subgroups of solvable orderable groups. (English. Russian original) Zbl 1245.20049

Bludov, V. V.; Kopytov, V. M.; Rhemtulla, A. H.

Algebra Logic 48, No. 3, 163-172 (2009); translation from Algebra Logika 48, No. 3, 291-308 (2009).

Summary: Orderable solvable groups in which every relatively convex subgroup is normal are studied. If such a class is subgroup closed, then it is precisely the class of solvable orderable groups which are locally of finite (Mal’tsev) rank. A criterion for an orderable metabelian group to have every relatively convex subgroup normal is given. Examples of an orderable solvable group \(G\) of length three with periodic \(G/G'\) and of an orderable solvable group of length four with only one proper normal relatively convex subgroup are constructed.

MSC:

20F60	Ordered groups (group-theoretic aspects)
20E07	Subgroup theorems; subgroup growth
20F16	Solvable groups, supersolvable groups
06F15	Ordered groups

Keywords:

ordered groups; orderable solvable groups; normal relatively convex subgroups; orderable metabelian groups

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