  In this paper we establish some subnormal embeddings of groups into groups
with additional properties; in particular embeddings of countable groups into
2-generated groups with some extra properties. The results obtained are
generalizations of theorems of P. Hall, R. Dark, B. Neumann, Hanna Neumann, G.
Higman on embeddings of that type. Considering subnormal embeddings of finite
groups into finite groups with additional properties we bring some illustration
to a result of H. Heineken and J. Lennox.
