Corpus ID: 235731726

Homology of the pronilpotent completion and cotorsion groups

  title={Homology of the pronilpotent completion and cotorsion groups},
  author={Mikhail Basok and Sergei O. Ivanov and Roman Mikhailov},
For a non-cyclic free group F , the second homology of its pronilpotent completion H2(F̂ ) is not a cotorsion group. 


On the third homotopy group of Orr’s space
K. Orr defined a Milnor-type invariant of links that lies in the third homotopy group of a certain space $K_\omega.$ The problem of non-triviality of this third homotopy group has been open. We showExpand
On a problem of Bousfield for metabelian groups
Abstract The homological properties of localizations and completions of metabelian groups are studied. It is shown that, for R = Q or R = Z / n and a finitely presented metabelian group G, theExpand
Link concordance invariants and homotopy theory
SummaryWe show that each of a sequence of concordance invariants for codimension-two links of spheres inSn+2, defined by Kent Orr, is identically zero forn>1. For classical links (n=1), the sameExpand
On Cotorsion Images of the Baer-Specker Group
A paper in the Bulletin [1] some years ago has discussed in detail the so-called Baer–Specker group P , the full Cartesian product of countably many copies of the integers, Z. Despite its seeminglyExpand
On discrete homology of a free pro- $p$ -group
For a prime $p$ , let $\hat{F}_{p}$ be a finitely generated free pro- $p$ -group of rank at least $2$ . We show that the second discrete homology group $H_{2}(\hat{F}_{p},\mathbb{Z}/p)$ is anExpand
On homology of Lie algebras over commutative rings
We study five different types of the homology of a Lie algebra over a commutative ring which are naturally isomorphic over fields. We show that they are not isomorphic over commutative rings, evenExpand
The abelianization of inverse limits of groups
The abelianization is a functor from groups to abelian groups, which is left adjoint to the inclusion functor. Being a left adjoint, the abelianization functor commutes with all small colimits. InExpand
Some groups that are just about free
A system for determining if ocean dumping of waste materials by licensed vessels occurs in other than assigned areas utilizes Loran receiving means for providing electrical signals indicative of theExpand
Homological properties of parafree Lie algebras
Abstract In this paper, an explicit construction of a countable parafree Lie algebra with nonzero second homology is given. It is also shown that the cohomological dimension of the pronilpotentExpand
A finite Q-bad space
  • Geometry & Topology
  • 2019