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Constructive Abelian \(p\)-groups. (English. Russian original) Zbl 0854.03037
Sib. Adv. Math. 2, No. 2, 68-113 (1992); translation from Tr. Inst. Mat. SO RAN 25, 155-199 (1993).
The author finds a necessary and sufficient condition for a countable abelian \(p\)-group which is not the direct sum of cyclic and quasi-cyclic groups to be (strongly) constructivizable. This gives also a condition for an abelian \(p\)-group whose reduced part has finite Ulm type to be (strongly) constructivizable. Every finite direct power of such a group \(G\) is (strongly) constructivizable iff \(G\) is (strongly) constructivizable.

03C57 Computable structure theory, computable model theory
20K10 Torsion groups, primary groups and generalized primary groups
03D45 Theory of numerations, effectively presented structures
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