Abstract
We consider the lattices of fully invariant subgroups of cotorsion hulls for different classes of separable primary Abelian groups. Based on the results of A. Mader, A. I. Moskalenko, A. L. S. Corner, and R. S. Pierce, these lattices are discussed in situations, where the primary group is a direct sum of cyclic p-groups, a direct sum of torsion-complete groups, or an additive group of the primary group of ring endomorphisms is a direct sum of a group of small endomorphisms and a p-adic completion of a direct sum of infinite cyclic groups. The questions concerning the full transitivity of a cotorsion hull are discussed.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 177, Algebra, 2020.
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Kemoklidze, T. The Lattice of Fully Invariant Subgroups of a Cotorsion Hull. J Math Sci 275, 744–748 (2023). https://doi.org/10.1007/s10958-023-06716-3
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DOI: https://doi.org/10.1007/s10958-023-06716-3