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AN EXTENSION OF A RESULT OF A. D. SANDS

AN EXTENSION OF A RESULT OF A. D. SANDS DEMONSTRATIO MATHEMATICAVol. XXXIIINo 32000Sandor SzaboA N EXTENSION OF A RESULT OF A. D. SANDSA b s t r a c t . A. D. Sands showed that if a group of type (2 2 , 2 2 ) is a direct product ofits subsets of order 4, then at least one of these subsets must be periodic. In this paperwe prove a result about groups of type (2^,2^) that generalizes Sands' theorem.1. IntroductionIn this paper we will use multiplicative notation in connection with finiteabelian groups. If A and B are subsets of a finite abelian group G such thatthe product AB is direct and is equal to G we say that AB is a factorizationof G. We also say that the equation G = AB is a factorization of G. Inother words the product AB is a factorization of G if each element g in G isuniquely expressible in the form g = ab, where a G A and b € B. In the mostcommonly encountered situation A and B are subgroups of G. However, inthis paper we do not assume that A and B are subgroups of G. A subset Aof a finite abelian group G is called http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

AN EXTENSION OF A RESULT OF A. D. SANDS

Demonstratio Mathematica , Volume 33 (3): 8 – Jul 1, 2000

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Publisher
de Gruyter
Copyright
© by Sandor Szabó
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2000-0304
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXXIIINo 32000Sandor SzaboA N EXTENSION OF A RESULT OF A. D. SANDSA b s t r a c t . A. D. Sands showed that if a group of type (2 2 , 2 2 ) is a direct product ofits subsets of order 4, then at least one of these subsets must be periodic. In this paperwe prove a result about groups of type (2^,2^) that generalizes Sands' theorem.1. IntroductionIn this paper we will use multiplicative notation in connection with finiteabelian groups. If A and B are subsets of a finite abelian group G such thatthe product AB is direct and is equal to G we say that AB is a factorizationof G. We also say that the equation G = AB is a factorization of G. Inother words the product AB is a factorization of G if each element g in G isuniquely expressible in the form g = ab, where a G A and b € B. In the mostcommonly encountered situation A and B are subgroups of G. However, inthis paper we do not assume that A and B are subgroups of G. A subset Aof a finite abelian group G is called

Journal

Demonstratio Mathematicade Gruyter

Published: Jul 1, 2000

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