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1Department of Mathematics, University of Duisburg-Essen, Campus Essen, 45117 Essen, Germany and Einstein Institute of Mathematics, Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel. Daniel.Herden@uni-due.de
2Einstein Institute of Mathematics, Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel and Center for Mathematical Sciences Research, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019 USA. Shelah@math.huji.ac.il
Citation Information: Forum Mathematicum. Volume 22, Issue 4, Pages 627–640, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/forum.2010.034, February 2010
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.
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