Weak commutativity and finiteness properties of groups
نویسندگان
چکیده
منابع مشابه
On Commutativity and Finiteness in Groups
The second author introduced notions of weak permutablity and commutativity between groups and proved the finiteness of a group generated by two weakly permutable finite subgroups. Two groups H, K weakly commute provided there exists a bijection f : H → K which fixes the identity and such that h commutes with its image h for all h ∈ H. The present paper gives support to conjectures about the ni...
متن کاملHomological and Finiteness Properties of Picture Groups
Picture groups are a class of groups introduced by Guba and Sapir. Known examples include Thompson’s groups F , T , and V . In this paper, a large class of picture groups is proved to be of type F∞. A Morse-theoretic argument shows that, for a given picture group, the rational homology vanishes in almost all dimensions.
متن کاملJumping loci and finiteness properties of groups
Characteristic varieties. Let X be a connected CW-complex with finitely many cells in each dimension, and G its fundamental group. The characteristic varieties of X are the jumping loci for cohomology with coefficients in rank 1 local systems: V i k (X) = {ρ ∈ Hom(G,C∗) | dimH(X,Cρ) ≥ k}. These varieties emerged from the work of Novikov [22] on Morse theory for closed 1-forms on manifolds. It t...
متن کاملA commutativity-or-finiteness condition for rings
In view of this result, it was conjectured that any ring with only finitely many noncentral subrings is either finite or commutative. It is our principal goal to prove this conjecture; and in the process we provide a new proof of Theorem 1.1. For any ring R, the symbols N, D, Z , and ℘(R) will denote, respectively, the set of nilpotent elements, the set of zero divisors, the center, and the pri...
متن کاملImproving Finiteness Properties for Metabelian Groups
We show that any finitely generated metabelian group can be embedded in a metabelian group of type F3. The proof builds upon work of G. Baumslag [4], who independently with V. R. Remeslennikov [10] proved that any finitely generated metabelian group can be embedded in a finitely presented one. We also rely essentially on the Sigma theory of R. Bieri and R. Strebel [7], who introduced this geome...
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: Bulletin of the London Mathematical Society
سال: 2018
ISSN: 0024-6093
DOI: 10.1112/blms.12219