On embeddings of countable generalized soluble groups into two-generated groups

JOURNAL OF ALGEBRA

卷:250

Article

Mikaelian, VH

关键词: embeddings of groups ordered groups;    generalized soluble groups;    normal and subnormal systems;    ascending and descending series;    two-generated groups;   

DOI  :  10.1006/jabr.2002.9047

来源: Elsevier

【 摘 要 】

Strengthening a theorem of L. G. Kovacs 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 subset of or equal to F-infinity 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. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free