Torsion-Free Space Groups, 2-Cohomology, and Scott Modules
نویسندگان
چکیده
منابع مشابه
Torsion-free Abelian Groups with Optimal Scott Families
We prove that for any computable successor ordinal of the form α = δ + 2k (δ limit and k ∈ ω) there exists computable torsion-free abelian group (TFAG) that is relatively ∆α-categorical and not ∆ 0 α−1-categorical. Equivalently, for any such α there exists a computable TFAG whose initial segments are uniformly described by Σα infinitary computable formulae up to automorphism (i.e., has a c.e. u...
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A discrete group G has periodic cohomology over R if there is an element α ∈ Ext RG (R,R) of positive degree and an integer n ≥ 0 such that the cup product map by α induces an isomorphism of Ext RG (R,−) and Ext i+|α| RG (R,−) for i ≥ n. Adem and Smith [1] showed if R = Z, then this condition is equivalent to the existence of a finite dimensional free-G-CW-complex homotopy equivalent to a spher...
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For every prime integer p, M. Hochster conjectured the existence of certain p-torsion elements in a local cohomology module over a regular ring of mixed characteristic. We show that Hochster’s conjecture is false. We next construct an example where a local cohomology module over a hypersurface has p-torsion elements for every prime integer p, and consequently has infinitely many associated prim...
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Let G be a finite group and let T (G) be the abelian group of equivalence classes of endotrivial kG-modules, where k is an algebraically closed field of characteristic p. We investigate the torsion-free part TF (G) of the group T (G) and look for generators of TF (G). We describe three methods for obtaining generators. Each of them only gives partial answers to the question but we obtain more p...
متن کامل`2–torsion of Free-by-cyclic Groups
We provide an upper bound on the `2–torsion of a free-bycyclic group, −ρ(2)(F oΦ Z), in terms of a relative train-track representative for Φ ∈ Aut(F). Our result shares features with a theorem of Lück–Schick computing the `2–torsion of the fundamental group of a 3–manifold that bers over the circle in that it shows that the `2–torsion is determined by the exponential dynamics of the monodromy. ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1996
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0100