324 citations · 1.7k across the 753 of their papers we have counts for
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GCH implies the existence of many rigid almost free abelian groups
Rüdiger Göbel, Saharon Shelah
We begin with the existence of groups with trivial duals for cardinals aleph_n (n in omega). Then we derive results about strongly aleph_n-free abelian groups of cardinality aleph_…
Outer Automorphism Groups of Ordered Permutation Groups
Manfred Droste, Saharon Shelah
An infinite linearly ordered set (S,<=) is called doubly homogeneous if its automorphism group A(S) acts 2-transitively on it. We show that any group G arises as outer automorphism…
Radicals and Plotkin's problem concerning geometrically equivalent groups
Rüdiger Göbel, Saharon Shelah
If G and X are groups and N is a normal subgroup of X, then the G-closure of N in X is the normal subgroup X^G= bigcap{kerphi|phi:X-> G, with N subseteq kerphi} of X . In particula…
Philip Hall's Problem On Non-Abelian Splitters
Rüdiger Göbel, Saharon Shelah
Philip Hall raised around 1965 the following question which is stated in the Kourovka Notebook: Is there a non-trivial group which is isomorphic with every proper extension of itse…
Localizations of Groups
Rüdiger Göbel, Saharon Shelah
A group homomorphism eta:A-> H is called a localization of A if every homomorphism phi:A-> H can be `extended uniquely' to a homomorphism Phi:H-> H in the sense that Phi eta = phi.…
Groups isomorphic to all their non-trivial normal subgroups
Rüdiger Göbel, Agnes T. Paras, Saharon Shelah
In answer to a question of P. Hall, we supply another construction of a group which is isomorphic to each of its non-trivial normal subgroups.