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COLLOQUIA PATAVINA

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When is an abelian group free abelian?

Laszlo Fuchs
Tulane University, New Orleans

7.6.2011



Abstract
There are several important problems that ask whether some abelian group is free (as an abelian group).  We will view several problems of this kind. Interestingly, some lead to undecidability results. The groups we will discuss include groups with discrete norm, as well as Baer and Whitehead groups. Recall that A is a Baer group if Ext(A, T)=0 for all torsion groups T, and is a Whitehead group if Ext(A, Z)=0 for the infinite cyclic group Z.  A few applications as well as generalizations to modules will also be mentioned.