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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
Demonstratio Mathematica – de Gruyter
Published: Jul 1, 2000
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