When is an abelian group free abelian?
Tulane University, New Orleans
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.