Torsion cohomology for solvable groups of finite rank

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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
StatePublished - May 1 2015

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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