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A characterization of Ext(G,ℤ) assuming (V = L)

Saharon Shelah, Lutz Strüngmann (2007)

Fundamenta Mathematicae

We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence ( ν p : p ∈ Π ) of cardinals satisfying ν p ≤ 2 ν (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that ν p equals the p-rank of Ext(G,ℤ) for every...

A characterization of Fuchsian groups acting on complex hyperbolic spaces

Xi Fu, Liulan Li, Xiantao Wang (2012)

Czechoslovak Mathematical Journal

Let G ⊂ 𝐒𝐔 ( 2 , 1 ) be a non-elementary complex hyperbolic Kleinian group. If G preserves a complex line, then G is ℂ -Fuchsian; if G preserves a Lagrangian plane, then G is ℝ -Fuchsian; G is Fuchsian if G is either ℂ -Fuchsian or ℝ -Fuchsian. In this paper, we prove that if the traces of all elements in G are real, then G is Fuchsian. This is an analogous result of Theorem V.G. 18 of B. Maskit, Kleinian Groups, Springer-Verlag, Berlin, 1988, in the setting of complex hyperbolic isometric groups. As an application...

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