Factoring by subsets of cardinality of prime power

K. Corrádi; S. Szabó

doi:10.1007/bf01875973

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 26: Issue 3

Factoring by subsets of cardinality of prime power

Authors:

K. Corrádi

K. Corrádi Department of Computer Sciences Eötvös University Budapest H-1088 Budapest Hungary

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and

S. Szabó

S. Szabó Department of Mathematics Faculty of Civil Engineering Technical University Budapest H-1521 Budapest Hungary

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Pages:: 201–204

Online Publication Date:: 03 Jul 2005

Publication Date:: 01 Jun 1993

Article Category:: Research Article

DOI:: https://doi.org/10.1007/bf01875973

Keywords:: Primary 20K01; Secondary 52C22

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Rédei's theorem asserts that if a finite abelian group is expressed as a direct product of subsets of prime cardinality, then at least one of the factors must be periodic. (A periodic subset is a direct product of some subset and a nontrivial subgroup.) A. D. Sands proved that if a finite cyclic group is the direct product of subsets each of which has cardinality that is a power of a prime, then at least one of the factors is periodic. We prove that the same conclusion holds if a general finite abelian group is factored as a direct product of cyclic subsets of prime cardinalities and general subsets of cardinalities that are powers of primes provided that the components of the group corresponding to these latter primes are cyclic.

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)