Torsion cohomology for solvable groups of finite rank

Research output: Contribution to journalArticle

Abstract

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 generated. Assume that G is a group in U and A a ZG-module. If A is Z-torsion-free and has finite Z-rank, we stipulate a condition on A that guarantees that Hn(G, A) and Hn(G, A) must be finite for n≥0. Moreover, if the underlying abelian group of A is a Černikov group, we identify a similar condition on A that ensures that Hn(G, A) must be a Černikov group for all n≥0.

Original languageEnglish (US)
Pages (from-to)447-464
Number of pages18
JournalJournal of Algebra
Volume429
DOIs
StatePublished - May 1 2015

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Solvable Group
Finite Rank
Torsion
Cohomology
Torsion-free
Finitely Generated
Abelian group
Module

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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abstract = "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 generated. Assume that G is a group in U and A a ZG-module. If A is Z-torsion-free and has finite Z-rank, we stipulate a condition on A that guarantees that Hn(G, A) and Hn(G, A) must be finite for n≥0. Moreover, if the underlying abelian group of A is a Černikov group, we identify a similar condition on A that ensures that Hn(G, A) must be a Černikov group for all n≥0.",
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Torsion cohomology for solvable groups of finite rank. / Lorensen, Karl.

In: Journal of Algebra, Vol. 429, 01.05.2015, p. 447-464.

Research output: Contribution to journalArticle

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