1,721,001 research outputs found
Centralisers of finite subgroups in soluble groups of type FPn
No full textWe show that for soluble groups of type FPn , centralisers of finite subgroups need not be of type FPn<br/
Complete Bredon cohomology and its applications to hierarchically defined groups
Full text linkBy considering the Bredon analogue of complete cohomology of a group, we show that every group in the class \LHFF of type Bredon-\FP_\infty admits a finite dimensional model for \EFG.We also show that abelian-by-infinite cyclic groups admit a 3-dimensional model for the classifying space for the family of virtually nilpotent subgroups. This allows us to prove that for \mF, the class of virtually cyclic groups, the class of \LHFF-groups contains all locally virtually soluble groups and all linear groups over C of integral characteristic
Is there an algebraic characterisation for finite-dimensional proper G-spaces?
No full textWe shall study properties of groups having finite cohomological dimension relative to the family of all finite subgroups. We also compare these groups with those satisfying various suggested algebraic analogues to group-actions on finite dimensional proper G-spaces
Complete cohomology for arbitrary rings using injectives
No full textWe will develop a complete cohomology theory, which vanishes on injectives and give necessary and sufficient conditions for it to be equivalent to the generalized Tate cohomology theory developed by Mislin, Benson and Carlson and Vogel
Virtually soluble groups of type FP?
Full text linkWe prove that a soluble group G of type FP? admits a finitely dominated model for a classifying space for proper actions of dimension the Hirsch length of G. This implies in particular that the Brown conjecture is satisfied for virtually torsion-free soluble groups.<br/
On groups acting on contractible spaces with stabilizers of prime power order
Full text linkLet F denote the class of finite groups, and let P denote the subclass consisting of groups of prime power order. We study group actions on topological spaces in which either (1) all stabilizers lie in P or (2) all stabilizers lie in F. We compare the classifying spaces for actions with stabilizers in F and P, the Kropholler hierarchies built on F and P, and group cohomology relative to F and to P. In terms of standard notations, we show that F C H1P C H1F, with all inclusions proper; that HF = HP; that FH*(G;?) = PH*(G;?); and that EpG is finite-dimensional if and only if EfG is finite-dimensional and every finite subgroup of G is in
On Bredon homology for elementary amenable groups
Full text linkWe show that for elementary amenable groups the Hirsch length is equal to the Bredon homological dimension. This also implies that countable elementary amenable groups admit a finite-dimensional model for of dimension less than or equal to the Hirsch length plus one. Some remarks on groups of type are also made.<br/
Some groups of type VF
No full textA group is of type VF if it contains a finite-index subgroup which has a finite classifying space. We construct groups of type VF in which the centralizers of some elements of finite order are not of type VF and groups of type VF containing infinitely many conjugacy classes of finite subgroups. From these examples it follows that a group G of type VF need not admit a finite-type or finite classifying space for proper actions (sometimes also called the universal proper G-space). We construct groups G for which the minimal dimension of a universal proper G-space is strictly greater than the virtual cohomological dimension of G. Each of our groups embeds in some general linear group over the rational integers. Applications to algebraic K-theory of group algebras and topological K-theory of group C*-algebras are also considered. The groups are constructed as finite extensions of Bestvina-Brady groups
Cohomological dimension of Mackey functors for infinite groups
Full text linkWe consider the cohomology of Mackey functors for infinite groups and define the Mackey-cohomological dimension of a group G. We relate this dimension to other cohomological dimensions such as the Bredon cohomological dimension and the relative cohomological dimension. In particular we show that for virtually torsion free groups the Mackey cohomological dimension is equal to both the relative cohomological dimension and the virtual cohomological dimension.<br/
Cohomology relative to a G-set and finiteness conditions
No full textWe shall consider a cohomology theory relative to group actions on sets and develop a completion analogous to Mislin, Benson and Carlson. Later we restrict ourselves to cohomology relative to all finite subgroups. There we shall study relative analogues to finiteness conditions on kG-modules such as finite relative projective dimension and being of relative type FP
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