K. Lorensen

activity

20082025

most citedGroups with the same cohomology as their pro-

p

completions

2 citations · 4 across the 8 of their papers we have counts for

collaborators

11 papers

math.RA2025

The rank condition and strong rank conditions for Ore extensions

Karl Lorensen, Johan Öinert

Let $R$ be a ring, $σ : R \to R$ a ring endomorphism, and $δ : R \to R$ a $σ$ -derivation. We establish that the Ore extension $R [x; σ, δ]$ satisfies the rank condition if and only if $R$ d…

math.RA2024

Rank conditions and amenability for rings associated to graphs

Karl Lorensen, Johan Öinert

We study path rings, Cohn path rings, and Leavitt path rings associated to directed graphs, with coefficients in an arbitrary ring $R$ . For each of these types of rings, we stipula…

math.RA2022

Generating numbers of rings graded by amenable and supramenable groups

Karl Lorensen, Johan Öinert

A ring $R$ has {\it unbounded generating number} (UGN) if, for every positive integer $n$ , there is no $R$ -module epimorphism $R^{n} \to R^{n + 1}$ . For a ring $R=\bigoplus_{g\in G} R_g…

math.RA2019

Group-graded rings satisfying the strong rank condition

Peter Kropholler, Karl Lorensen

A ring $R$ satisfies the {\it strong rank condition} (SRC) if, for every natural number $n$ , the free $R$ -submodules of $R^{n}$ all have rank $\leq n$ . Let $G$ be a group and $R$ a r…

math.GR2015★ 1 cited

Virtually torsion-free covers of minimax groups

Peter Kropholler, Karl Lorensen

We prove that every finitely generated, virtually solvable minimax group can be expressed as a homomorphic image of a virtually torsion-free, virtually solvable minimax group. This…

math.GR2014

Torsion cohomology for solvable groups of finite rank

Karl Lorensen

We define a class $U$ of solvable groups of finite abelian section rank which includes all such groups that are virtually torsion-free as well as those that are finitely…

math.GR2013★ 1 cited

The cohomology of virtually torsion-free solvable groups of finite rank

Peter Kropholler, Karl Lorensen

Assume that $G$ is a virtually torsion-free solvable group of finite rank and $A$ a $Z G$ -module whose underlying abelian group is torsion-free and has finite rank. We stipu…

math.GR2011

Cohomology and profinite topologies for solvable groups of finite rank

Karl Lorensen

Assume $G$ is a solvable group whose elementary abelian sections are all finite. Suppose, further, that $p$ is a prime such that $G$ fails to contain any subgroups isomorphic to $C…

math.GR2010

Ascending HNN extensions of polycyclic groups have the same cohomology as their profinite completions

Karl Lorensen

Assume $G$ is a polycyclic group and $ϕ : G \to G$ an endomorphism. Let $G *_{ϕ}$ be the ascending HNN extension of $G$ with respect to $ϕ$ ; that is, $G *_{ϕ}$ is given by the present…

math.GR2008★ 2 cited

Groups with the same cohomology as their pro- $p$ completions

Karl Lorensen

For any prime $p$ and group $G$ , denote the pro- $p$ completion of $G$ by $G^^{p}$ . Let $C$ be the class of all groups $G$ such that, for each natural number $n$ and pr…

math.GR2008

Groups with the same cohomology as their profinite completions

Karl Lorensen

For any positive integer $n$ , $A_{n}$ is the class of all groups $G$ such that, for $0 \leq i \leq n$ , $H^{i} (G^, A) ≅ H^{i} (G, A)$ for every finite discrete $G^$ -modu…

The rank condition and strong rank conditions for Ore extensions

Rank conditions and amenability for rings associated to graphs

Generating numbers of rings graded by amenable and supramenable groups

Group-graded rings satisfying the strong rank condition

Virtually torsion-free covers of minimax groups

Torsion cohomology for solvable groups of finite rank

The cohomology of virtually torsion-free solvable groups of finite rank

Cohomology and profinite topologies for solvable groups of finite rank

Ascending HNN extensions of polycyclic groups have the same cohomology as their profinite completions

Groups with the same cohomology as their pro-p completions

Groups with the same cohomology as their profinite completions

Groups with the same cohomology as their pro- $p$ completions