Affiliation:
1. School of Mathematics and Statistics , University of Sydney , Syndney , NSW 2006 , Australia
Abstract
Abstract
We show that torsion-free elementary amenable groups of Hirsch length at most 3 are solvable, of derived length at most 3.
This class includes all solvable groups of cohomological dimension 3.
We show also that groups in the latter subclass are either polycyclic, semidirect products
BS
(
1
,
n
)
⋊
Z
\mathrm{BS}(1,n)\rtimes\mathbb{Z}
, or properly ascending HNN extensions with base
Z
2
\mathbb{Z}^{2}
or
π
1
(
Kb
)
\pi_{1}(\mathrm{Kb})
.
Subject
Algebra and Number Theory
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