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Cohomological Finiteness Conditions in B...
Kochloukova, D. H....

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Cohomological Finiteness Conditions in Bredon Cohomology by Kochloukova, D. H. ( Author )
Lemonjar Open Access
N.A
24-03-2009
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≤3 and restrict to abelian-by-nilpotent, abelian-by-polycyclic or (nilpotent of class 2)-by-abelian groups.
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/0903.4079
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