On quasiresolvent periodic abelian groups
Copyright policy )On quasiresolvent periodic abelian groups
Summary: This is a continuation of the author's paper [Algebra Logika 43, No. 5, 614-628 (2004; Zbl 1095.03022); translation in Algebra Logic 43, No. 5, 346-354 (2004)]. We introduce the concept of a primarily quasiresolvent periodic Abelian group and describe primarily quasiresolvent and 1-quasiresolvent periodic Abelian groups. We construct an example of a quasiresolvent but not primarily quasiresolvent periodic Abelian group. For a direct sum of primary cyclic groups we obtain criteria for a group to be quasiresolvent, 1-quasiresolvent, and resolvent, and establish relations among them. We construct a set \(S\) of primes such that the direct sum of some cyclic groups of orders \(p\in S\) is not a quasiresolvent group.
- Sobolev Institute of Mathematics Russian Federation
primary quasiresolvent groups, computability, Direct sums, direct products, etc. for abelian groups, periodic Abelian groups, Computable structure theory, computable model theory, admissible sets, Torsion groups, primary groups and generalized primary groups
primary quasiresolvent groups, computability, Direct sums, direct products, etc. for abelian groups, periodic Abelian groups, Computable structure theory, computable model theory, admissible sets, Torsion groups, primary groups and generalized primary groups
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