J. Aust. Math. Soc.  74 (2003), 379-392
An embedding construction for ordered groups

Vahagn H. Mikaelian
  Department of Informatics and Computer Science
  Yerevan State University
  375025 Yerevan

Generalizing and strengthening some well-known results of Higman, B. Neumann, Hanna Neumann and Dark on embeddings into two-generator groups, we introduce a construction of subnormal verbal embedding of an arbitrary (soluble, fully ordered or torsion free) ordered countable group into a two-generator ordered group with these properties. Further, we establish subnormal verbal embedding of defect two of an arbitrary (soluble, fully ordered or torsion free) ordered group G into a group with these properties and of the same cardinality as G, and show in connection with a problem of Heineken that the defect of such an embedding cannot be made smaller, that is, such verbal embeddings of ordered groups cannot in general be normal.
Download the article in PDF format (size 114 Kb)

TeXAdel Scientific Publishing ©  Australian MS