The Athens Algebra Seminar presents “Whitehead’s conjecture is undecidable in ZFC” by Shehzad Ahmed on Thursday, Nov. 12, from 4:35-5:30 p.m. in Morton 218.
Abstract: We say that an abelian group A is a W-group if, given any surjective homomorphism pi: B \rightarrow A of abelian groups with kernel \mathbb Z, there is a homomorphism \rho : A \rightarrow B such that \pi \rho is the identity on A (i.e.\pi splits). This is equivalent to saying that the only extension of A by \mathbb Z is (up to isomorphism) A \oplus Z, or rather that Ext^1_{\mathbb Z}(A; {\mathbb Z}) = 0 in the language of homological algebra. It’s relatively simple to show that every free abelian group is a W-group, and Whitehead’s conjecture asks whether or not the reverse is true. The goal of this talk is to use Whitehead’s conjecture to explain the notion of independence, and will be targeted at graduate students with a moderate background in group theory. The set-theoretic prerequisites will be kept to a minimum, and I will introduce anything from set theory that we need along the way.
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