Embeddings into pro-p groups and the construction of parafree groups

TL;DR

This paper characterizes when certain group constructions, like amalgamated products and HNN extensions, produce parafree groups, which are residually nilpotent and share nilpotent quotients with free groups.

Contribution

It provides new criteria for parafreeness in groups formed via amalgamated products and HNN extensions, advancing understanding of their algebraic structure.

Findings

Parafreeness characterized for amalgamated products with cyclic amalgams.

Parafreeness characterized for cyclic HNN extensions.

Provides criteria to identify parafree groups in these constructions.

Abstract

A finitely generated group G is termed parafree if it is residually nilpotent and it has the same isomorphism types of nilpotent quotients as some free group. The two main results of this MSc. Thesis characterise the parafreeness of two constructions, namely amalgamated products with cyclic amalgams and cyclic HNN extensions.