Homology of the pronilpotent completion and cotorsion groups

TL;DR

This paper investigates the homological properties of the pronilpotent completion of free groups, revealing that for non-cyclic free groups, the second homology group is not cotorsion.

Contribution

It demonstrates that the second homology of the pronilpotent completion of non-cyclic free groups is not cotorsion, providing new insights into their algebraic structure.

Findings

Second homology of pronilpotent completion is not cotorsion for non-cyclic free groups

Highlights differences between free groups and their completions in homological properties

Contributes to understanding of algebraic and homological characteristics of free groups

Abstract

For a non-cyclic free group $F$, the second homology of its pronilpotent completion $H_2(\widehat F)$ is not a cotorsion group.