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An abelian group G of type 0 is called κ-fold transitive for some cardinal κ > 0 if for any pair of pure elements x, y ∈ G there exist exactly κ-many φ ∈ Aut G such that xφ = y. We show the existence of large κ-fold transitive groups for every κ ≥ ℵ0 assuming V=L and ZFC respectively.
Published Online: 2010-02-08
Published in Print: 2010-July