Torsion cohomology for solvable groups of finite rank

Abstract

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 $\mathbb{Z}G$-module. If $A$ is $\mathbb{Z}$-torsion-free and has finite $\mathbb{Z}$-rank, we stipulate a condition on $A$ that guarantees that $H^n(G,A)$ and $H_n(G,A)$ must be finite for $n\ge 0$. Moreover, if the underlying abelian group of $A$ is a Černikov group, we identify a similar condition on $A$ that ensures that $H^n(G,A)$ must be a Černikov group for all $n\ge 0$.

arXiv commentTo appear in Journal of Algebra

References in corpus (1)

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