On Embeddings of Countable Generalized Soluble Groups into Two-Generated Groups

Strengthening a theorem of L. G. Kovács and B. H. Neumann on embeddings of countable SN*- and SI*-groups into two-generated SN*- and SI*-groups, we establish embeddability of fully ordered countable SN-, SN*-, SI-, and SI*- groups into appropriate fully ordered two-generated groups of the same type. Moreover, for an arbitrary non-trivial word set V F∞ the mentioned two-generated group can be chosen such that the verbal V-subgroup of the latter contains the order isomorphic copy of an initial countable group. These embeddings are subnormal but not, in general, normal.