Embedding construction based on amalgamations of group relators

Abstract

An embedding construction $G\hookrightarrow H$ for groups $G$ with a length function was introduced by the author earlier. Here we obtain new properties of this embedding, answering some questions raised by M.V. Sapir. In particular, an analog of Tits' alternative holds for the subgroups of $H$.

20 pages, 9 figures. extended version, added pictures, corrected typos