Coherence for elementary amenable groups
Sam Hughes, Dawid Kielak, Peter H. Kropholler, Ian J. Leary
该研究针对初等顺从群，证明群凝聚性、同调凝聚性与整群环凝聚性等价，推广了Bieri和Strebel关于有限生成可解群的相关结论。
我们证明，对于初等顺从群而言，群的凝聚性、群的同调凝聚性以及整群环的凝聚性三者等价。这推广了Bieri与Strebel关于有限生成可解群的一项结果。
We prove that for an elementary amenable group, coherence of the group, homological coherence of the group, and coherence of the integral group ring are all equivalent. This generalises a result of Bieri and Strebel for finitely generated soluble groups.
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We prove that any finitely generated elementary amenable group of zero (algebraic) entropy contains a nilpotent subgroup of finite index or, equivalently, any finitely generated elementary amenable group of exponential growth is of uniformly exponential growth. We also show that 0 is an accumulation point of the set of entropies of elementary amenable groups.
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Elementary amenable groups of cohomological dimension 3
研究显示，余维数为3的无 torsion 初等可除群是可解群，导出长度不超过3。此类群包括所有余维数为3的可解群，且后者子类群要么是多项式群，要么是半直接积或恰当递增的 HNN 扩张。
Some elementary amenable subgroups of interval exchange transformations
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A finitely generated ICC non property (T) group that is neither inner amenable nor properly proximal
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