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

Peter Kropholler, Karl Lorensen

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Assume that G is a virtually torsion-free solvable group of finite rank and A is a ℤG-module whose underlying abelian group is torsion-free and has finite rank. We stipulate a condition on A that ensures that Hn(G,A) and Hn(G,A) are finite for all n ≥ 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.

Original languageEnglish (US)
Pages (from-to)6441-6459
Number of pages19
JournalTransactions of the American Mathematical Society
Volume367
Issue number9
DOIs
StatePublished - Jan 1 2015

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Torsion-free Group
Solvable Group
Finite Rank
Torsional stress
Cohomology
Homological Dimension
Torsion-free
Abelian group
Deduce
Two Dimensions
Complement
Module
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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The cohomology of virtually torsion-free solvable groups of finite rank. / Kropholler, Peter; Lorensen, Karl.

In: Transactions of the American Mathematical Society, Vol. 367, No. 9, 01.01.2015, p. 6441-6459.

Research output: Contribution to journalArticle

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