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- W2069173277 abstract "We show that any soluble group $G$ of type Bredon-$FP_{infty}$ with respect to the family of all virtually cyclic subgroups such that centralizers of infinite order elements are of type $FP_{infty}$ must be virtually cyclic. To prove this, we first reduce the problem to the case of polycyclic groups and then we show that a polycyclic-by-finite group with finitely many conjugacy classes of maximal virtually cyclic subgroups is virtually cyclic. Finally we discuss refinements of this result: we only impose the property Bredon-$FP_n$ for some $n leq 3$ and restrict to abelian-by-nilpotent, abelian-by-polycyclic or (nilpotent of class 2)-by-abelian groups." @default.
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- W2069173277 date "2010-10-29" @default.
- W2069173277 modified "2023-09-27" @default.
- W2069173277 title "Cohomological finiteness conditions in Bredon cohomology" @default.
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- W2069173277 doi "https://doi.org/10.1112/blms/bdq088" @default.
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