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math.GR2025
Failure of singular compactness for Hom
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
Assuming Gödel's axiom of constructibility , we construct a -free abelian group of singular cardinality for some suitable cardinal which is regular and uncountable,…
math.GR2025
Quite free p-groups with trivial duality
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
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, w…
math.GR2024
On groups well represented as automorphism groups of groups
Mohsen Asgharzadeh, Mohammad Golshani, Daniel Herden +1
Assuming Gödel's axiom of constructibility we present a characterization of those groups for which there exist arbitrarily large groups such that $aut(H)…