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<p>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 <i>p</i>-groups, for which we formulate and prove the <i>Trivial Duality Conjecture</i>. Key tools in our analysis include the multi black box method and the application of specific homological properties of relative trees.</p>

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Quite free p-groups with trivial duality

  • 期刊论文

  • 发表日期：

    2025年11月17日

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  • Mohsen Asgharzadeh,
  • Mohammad Golshani,
  • Saharon Shelah

摘要

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 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.