WebbTheorem A: A torsion-free group of cohomological dimension one over some ring with unit is free. Theorem B: A torsion-free group containing a free subgroup of finite index is free. … WebbActually, we show that this theorem can be derived easily from Stallings’s theorem for the p-lower central series. Here it is also obtained as a corollary of our main theorem …

Stallings

WebbTheorem A (Stallings). Every non-trivial free product P ∗F Q with amalgamated subgroup has a bipolar structure, and conversely, if G has a bipolar structure such that EE∗ has no irreducible elements, then G is a free product with amalgamation: G = P ∗F Q, where P, Q consist of the irreducible elements of EE, E∗E∗ respectively. WebbStallings-Zeeman theorem. In mathematics, the Stallings-Zeeman theorem is a result in algebraic topology, used in the proof of the Poincaré conjecture for dimension greater … town sports international human resources

Stallings-Zeeman theorem

Webb11 sep. 2024 · There is a coarse geometric characterisation analogous to Stallings's theorem of the property of splitting over an infinite cyclic subgroups due to Papasoglu, at least for finitely presented groups. This is the main result of his paper Quasi-Isometry Invariance of Group Splittings: Stallings' theorem was a starting point for Dunwoody's accessibility theory. A finitely generated group G {\displaystyle G} is said to be accessible if the process of iterated nontrivial splitting of G {\displaystyle G} over finite subgroups always terminates in a finite number of steps. Visa mer In the mathematical subject of group theory, the Stallings theorem about ends of groups states that a finitely generated group $${\displaystyle G}$$ has more than one end if and only if the group $${\displaystyle G}$$ admits … Visa mer Let $${\displaystyle G}$$ be a finitely generated group. Let $${\displaystyle S\subseteq G}$$ be a finite generating set of Visa mer • Free product with amalgamation • HNN extension • Bass–Serre theory Visa mer Let $${\displaystyle \Gamma }$$ be a connected graph where the degree of every vertex is finite. One can view $${\displaystyle \Gamma }$$ as a topological space by giving it the natural structure of a one-dimensional cell complex. … Visa mer • Among the immediate applications of Stallings' theorem was a proof by Stallings of a long-standing conjecture that every finitely generated … Visa mer Webbof a simple but powerful idea is Stallings’s beauti-ful paper “Topology of finite graphs”. How many people could write a deep paper with that title? In this paper Stallings took … town sports international inc