Quite free p-groups with trivial duality

Mohsen Asgharzadeh; Mohammad Golshani; Saharon Shelah

doi:10.1007/s00605-025-02145-3

Quite free p-groups with trivial duality

Mohsen Asgharzadeh
, Mohammad Golshani^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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 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.

Original language	English
Journal	Monatshefte fur Mathematik
DOIs	https://doi.org/10.1007/s00605-025-02145-3
State	Accepted/In press - 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025.

Keywords

Almost free groups
Relative trees
Set theoretical methods in algebra
Small morphism
Trivial duality problem
p-groups

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10.1007/s00605-025-02145-3

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Quite free p-groups with trivial duality

Abstract

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Keywords

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