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

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.

This MSc. Thesis was defended in July 2021 at Universidad Autónoma de Madrid and it was supervised by Andrei Jaikin-Zapirain. The author was supported by the Spanish Ministry of Science and Innovation through the grant JAE Intro SOMdM of the academic year 2020-2021