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

2021/09/25 by Ismael Morales, Morales, Ismael
Mathematics · #16K40 #20C07 #20E06 (Primary) #20E18 (Secondary) #20E26 #20J05 #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2109.12341

openalex publication_date 2021/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Virtually free pro-p products
• Free \mathbb Q-groups are residually torsion-free nilpotent
• Generalizing Magnus' characterization of free groups to some free products
• On some relatively free pro-p groups
• Parafree graphs of groups with cyclic edge groups