Výsledky vyhledávání - "Karl Lorensen"

Group-graded rings satisfying the strong rank condition

Autor: Peter H. Kropholler, Karl Lorensen

A ring $R$ satisfies the $\textit{strong rank condition}$ (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 ring strongly graded by $G$ such that the base ring $R_1$ is a dom

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

Autor: Peter H. Kropholler, Karl Lorensen

Publikováno v: Transactions of the American Mathematical Society. 367:6441-6459

Assume that $G$ is a virtually torsion-free solvable group of finite rank and $A$ a $\mathbb ZG$-module whose underlying abelian group is torsion-free and has finite rank. We stipulate a condition on $A$ that ensures that $H^n(G,A)$ and $H_n(G,A)$ ar

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https://doi.org/10.1090/s0002-9947-2015-06262-x

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Groups with the same cohomology as their profinite completions

Autor: Karl Lorensen

Publikováno v: Journal of Algebra. 320(4):1704-1722

For any positive integer $n$, $\mathcal{A}_n$ is the class of all groups $G$ such that, for $0\leq i\leq n$, $H^i(\hat{G},A)\cong H^i(G,A)$ for every finite discrete $\hat{G}$-module $A$. We describe certain types of free products with amalgam and HN

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Torsion cohomology for solvable groups of finite rank

Autor: Karl Lorensen

We define a class $\mathcal{U}$ 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 generated. Assume that $G$ is a group in $\mathcal{U}$ and $A$ a $\mat

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‘COHOMOLOGY AND PROFINITE TOPOLOGIES FOR SOLVABLE GROUPS OF FINITE RANK’

Autor: Karl Lorensen

Publikováno v: Bulletin of the Australian Mathematical Society. 91:351-352

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 $\mathbb Z/p^\infty$. We show that if $G$ is nilpotent, then the pro-$p$

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https://doi.org/10.1017/s0004972714001099

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Cohomology and profinite topologies for solvable groups of finite rank

Autor: 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 $C_{p^\infty}$. We show that if $G$ is nilpotent, then the pro-$p$ compl

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