The cohomology of virtually torsion-free solvable groups of finite rank
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- by Peter Kropholler and Karl Lorensen PDF
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Abstract:
Assume that $G$ is a virtually torsion-free solvable group of finite rank and $A$ is 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 $H_n(G,A)$ are finite for all $n\geq 0$. Using this property for cohomology in dimension two, we deduce two results concerning the presence of near supplements and complements in solvable groups of finite rank. As an application of our near-supplement theorem, we obtain a new result regarding the homological dimension of solvable groups.References
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Additional Information
- Peter Kropholler
- Affiliation: Mathematical Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
- MR Author ID: 203863
- ORCID: 0000-0001-5460-1512
- Email: P.H.Kropholler@southampton.ac.uk
- Karl Lorensen
- Affiliation: Department of Mathematics and Statistics, Pennsylvania State University, Altoona College, Altoona, Pennsylvania 16601
- Email: kql3@psu.edu
- Received by editor(s): March 19, 2013
- Received by editor(s) in revised form: April 1, 2013, and July 14, 2013
- Published electronically: March 13, 2015
- © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 6441-6459
- MSC (2010): Primary 20F16, 20J05, 20J06
- DOI: https://doi.org/10.1090/S0002-9947-2015-06262-X
- MathSciNet review: 3356943