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- Title
On quasiresolvent periodic abelian groups.
- Authors
Khisamiev, A. N.
- Abstract
This is a continuation of [1]. 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 ∈ S is not a quasiresolvent group.
- Subjects
ABELIAN groups; GROUP theory; ADMISSIBLE sets; ALGEBRA; MATHEMATICAL analysis; MATHEMATICAL research
- Publication
Siberian Mathematical Journal, 2007, Vol 48, Issue 6, p1115
- ISSN
0037-4466
- Publication type
Article
- DOI
10.1007/s11202-007-0113-2