Embedding construction based on amalgamations of group relators

TL;DR

This paper explores a novel embedding construction for groups with length functions, revealing new properties and answering open questions, including an analog of Tits' alternative for subgroups.

Contribution

It introduces new properties of a previously developed embedding construction, addressing open questions and extending understanding of subgroup structures.

Findings

An analog of Tits' alternative holds for subgroups of the constructed embedding.

New properties of the embedding construction are established.

The work answers specific questions raised by M.V. Sapir.

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 $H$.