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|Type:||Artigo de periódico|
|Title:||Cohomological finiteness conditions in Bredon cohomology|
|Abstract:||We show that soluble groups G of type Bredon-FP(infinity) with respect to the family of all virtually cyclic subgroups of G are always virtually cyclic. In such a group centralizers of elements are of type FP(infinity). We show that this implies that the group is polycyclic. Another important ingredient of the proof is 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.|
|Editor:||Oxford Univ Press|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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