Dimension of elementary amenable groups [article]

M. R. Bridson, P. H. Kropholler
2013 arXiv   pre-print
The paper has three parts. It is conjectured that for every elementary amenable group G and every non-zero commutative ring k, the homological dimension of G over k is equal to the Hirsch length of G whenever G has no k-torsion. In Part I this is proved for several classes, including the abelian-by-polycyclic groups. In Part II it is shown that elementary amenable groups of homological dimension one are filtered colimits of systems of groups of cohomological dimension one. Part III is devoted
more » ... the deeper study of cohomological dimension with particular emphasis on the nilpotent-by-polycyclic case.
arXiv:1208.1084v3 fatcat:sw3fo3ekwrgv3oa4pnrb3yguiu