Periodic flat resolutions and periodicity in group (co)homology

Javad Asadollahi; Ali Hajizamani; Shokrollah Salarian

doi:10.1515/form.2011.060

Article

Periodic flat resolutions and periodicity in group (co)homology

Javad Asadollahi , Ali Hajizamani and Shokrollah Salarian

Published/Copyright: February 25, 2012

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From the journal Volume 24 Issue 2

Abstract.

Using the notion of flat covers and proper flat resolutions, we study modules with periodic flat resolutions. It follows that, equivalently, we may study modules with periodic homology. We specialize our results to the category of modules over integral group ring , where is an arbitrary group. Among other results, we show that if a group is in a certain class of groups, then has periodic homology of period q after some steps with the periodicity isomorphisms of homology groups induced by the cap product with an element in Hq(,C), where C is the cotorsion envelope of the trivial -module , if and only if it has periodic cohomology of period q after some steps with the periodicity isomorphisms of cohomology groups induced by the cup product with an element in Hq(,).

Keywords.: Proper resolution; periodic flat resolution; homology of groups

Received: 2009-12-05

Revised: 2010-03-31

Published Online: 2012-02-25

Published in Print: 2012-March

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Articles in the same Issue

https://doi.org/10.1515/form.2011.060

Keywords for this article

Proper resolution; periodic flat resolution; homology of groups