Amenable groups of finite cohomological dimension and the zero divisor conjecture
نویسندگان
چکیده
We prove that every amenable group of cohomological dimension two whose integral ring is a domain solvable and investigate certain homological finiteness properties groups satisfy the analytic zero divisor conjecture act on an acyclic CW-complex with stabilisers.
منابع مشابه
Automorphisms of Pro-p groups of finite virtual cohomological dimension
Let G be a pro-p group of finite cohomological dimension and type FP∞ and T is a finite p-group of automorphisms of G. We prove that the group of fixed points of T in G is again a pro-p group of type FP∞ (in particular it is finitely presented). Moreover we prove that a pro-p group G of type FP∞ and finite virtual cohomological dimension has finitely many conjugacy classes of finite subgroups.
متن کاملNormal subgroups of profinite groups of finite cohomological dimension
We study a profinite group G of finite cohomological dimension with (topologically) finitely generated closed normal subgroup N . If G is pro-p and N is either free as a pro-p group or a Poincaré group of dimension 2 or analytic pro-p, we show that G/N has virtually finite cohomological dimension cd(G) − cd(N). Some other cases when G/N has virtually finite cohomological dimension are considere...
متن کاملThe Novikov conjecture and groups with finite asymptotic dimension ∗
Recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology [14]. More precisely, the asymptotic dimension for a metric space is the smallest integer n such that for any r > 0, there exists a uniformly bounded cover C = {Ui}i∈I of the metric space for which the rmultiplicity of C is at most n + 1, i.e. no ball of radius r in the metric space interse...
متن کاملFrom Acyclic Groups to the Bass Conjecture for Amenable Groups
We prove that the Bost Conjecture on the `-assembly map for countable discrete groups implies the Bass Conjecture. It follows that all amenable groups satisfy the Bass Conjecture.
متن کاملTHE ZERO-DIVISOR GRAPH OF A MODULE
Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, sayΓ(RM), such that when M=R, Γ(RM) coincide with the zero-divisor graph of R. Many well-known results by D.F. Anderson and P.S. Livingston have been generalized for Γ(RM). We Will show that Γ(RM) is connected withdiam Γ(RM)≤ 3 and if Γ(RM) contains a cycle, then Γ(RM)≤4. We will also show tha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2022
ISSN: ['1432-1807', '0025-5831']
DOI: https://doi.org/10.1007/s00208-022-02388-7