an:06051437
Zbl 1245.20049
Bludov, V. V.; Kopytov, V. M.; Rhemtulla, A. H.
Normal relatively convex subgroups of solvable orderable groups
EN
Algebra Logic 48, No. 3, 163-172 (2009); translation from Algebra Logika 48, No. 3, 291-308 (2009).
00302323
2009
j
20F60 20E07 20F16 06F15
ordered groups; orderable solvable groups; normal relatively convex subgroups; orderable metabelian groups
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.