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Type: Artigo de periódico
Title: Cohomological finiteness conditions in Bredon cohomology
Author: Kochloukova, DH
Martinez-Perez, C
Nucinkis, BEA
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.
Country: Inglaterra
Editor: Oxford Univ Press
Citation: Bulletin Of The London Mathematical Society. Oxford Univ Press, v. 43, n. 124, n. 136, 2011.
Rights: fechado
Identifier DOI: 10.1112/blms/bdq088
Date Issue: 2011
Appears in Collections:Unicamp - Artigos e Outros Documentos

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