Sh:1045a

• Asgharzadeh, M., Golshani, M., & Shelah, S. Quite free p-groups with trivial duality. Preprint. arXiv: 2503.07366
• Abstract:
  We present a class of abelian groups that exhibit a high degree of freeness while possessing no non-trivial homomorphisms to a canonical free object. Unlike prior investigations, which primarily focused on torsion-free groups, our work broadens the scope to include groups with torsion. Our main focus is on reduced separable p-groups, for which we formulate and prove the Trivial Duality Conjecture. Key tools in our analysis include the multi black-box method and the application of specific homological properties of relative trees. These techniques allow us to navigate the intricate interplay between freeness and duality in a broader class of abelian groups
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@article{Sh:1045a,
 author = {Asgharzadeh, Mohsen and Golshani, Mohammad and Shelah, Saharon},
 title = {{Quite free p-groups with trivial duality}},
 note = {\href{https://arxiv.org/abs/2503.07366}{arXiv: 2503.07366}},
 arxiv_number = {2503.07366}
}