A Class of Strongly Decomposable Abelian Groups
 N. G. Khisamiev
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Let G be a completely decomposable torsionfree Abelian group and G= ⊕ G_{i}, where G _{ i } is a rank 1 group. If there exists a strongly constructive numbering ν of G such that (G,ν) has a recursively enumerable sequence of elements g _{ i } ∈ G _{ i }, then G is called a strongly decomposable group. Let pi, i∈ω, be some sequence of primes whose denominators are degrees of a number p _{ i } and let \(\mathop \oplus \limits_{i \in \omega } Q_{Pi} \) . A characteristic of the group A is the set of all pairs ‹ p,k› of numbers such that \(p_{i_1 } = ... = p_{i_k } = p\) for some numbers i _{1},...,i_{ k }. We bring in the concept of a quasihyperhyperimmune set, and specify a necessary and sufficient condition on the characteristic of A subject to which the group in question is strongly decomposable. Also, it is proved that every hyperhyperimmune set is quasihyperhyperimmune, the converse being not true.
 A. I. Mal'tsev, “On recursive Abelian groups,” Dokl. Akad. NaukSSSR, 146, No. 5, 10091012 (1962).
 N. G. Khisamiev, “Constructiveabelian groups,” in Handbook of Recursive Mathematics, Vol. 2, Elsevier, Amsterdam (1998), pp. 11771230.
 N. G. Khisamiev and A. N. Krykpaeva, “Effectivelycompletely decomposable Abelian groups,” Sib. Mat. Zh., 38, No. 6, 14101412 (1997).
 N. G. Khisamiev, “Strongly constructive Abelian pgroups,” Algebra Logika,22, No. 2, 198217 (1983).
 N. G. Khisamiev, “Strongly completelydecomposable Abelian groups,” in Proc. Int. Conf. “Logic and Its Applications,” Novosibirsk (2000), p. 106.
 M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian],3d edn., Nauka, Moscow (1982).
 L. Fuchs, Infinite Abelian Groups, Vol. 1,Academic Press, New York (1970).
 Yu. L. Ershov, Problems of Decidability andConstructive Models [in Russian], Nauka, Moscow (1980).
 A. I. Mal'tsev,Algorithms and Recursive Functions [in Russian], Nauka, Moscow (1965).
 H. Rogers, Theory of Recursive Functions and Effective Computability, McGrawHill, New York (1967).
 Title
 A Class of Strongly Decomposable Abelian Groups
 Journal

Algebra and Logic
Volume 41, Issue 4 , pp 274283
 Cover Date
 20020701
 DOI
 10.1023/A:1020112806274
 Print ISSN
 00025232
 Online ISSN
 15738302
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 strongly decomposable Abelian group
 hyperhyperimmune set
 quasihyperhyperimmune set
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