### 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 H^{n}(G, A) and H_{n}(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 H^{n}(G, A) must be a Černikov group for all n≥0.

Original language | English (US) |
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Pages (from-to) | 447-464 |

Number of pages | 18 |

Journal | Journal of Algebra |

Volume | 429 |

DOIs | |

State | Published - May 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

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*Journal of Algebra*, vol. 429, pp. 447-464. https://doi.org/10.1016/j.jalgebra.2015.02.006

**Torsion cohomology for solvable groups of finite rank.** / Lorensen, Karl.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Torsion cohomology for solvable groups of finite rank

AU - Lorensen, Karl

PY - 2015/5/1

Y1 - 2015/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84923265402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923265402&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2015.02.006

DO - 10.1016/j.jalgebra.2015.02.006

M3 - Article

AN - SCOPUS:84923265402

VL - 429

SP - 447

EP - 464

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -