Quotient divisible groups of rank 2 M. N. Zonov, E. A. Timoshenko
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ArticleContent type: Текст Media type: электронный Subject(s): абелевы группы | факторно делимые группы | группы 2-рангаGenre/Form: статьи в журналах Online resources: Click here to access online
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Mathematical notes Vol. 110, № 1. P. 48-60Abstract: In the paper, representations of torsion-free Abelian groups of rank 2 using torsion-free groups of rank 1 are studied. Necessary and sufficient conditions are found under which a group given by such a representation is quotient divisible. A criterion is obtained for two p-minimal quotient divisible torsion-free groups of rank 2 to be isomorphic to each other. An example is constructed showing that two such groups can be embedded in each other but be nonisomorphic. A series of properties of fundamental systems of elements of quotient divisible groups of arbitrary finite rank is established.
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In the paper, representations of torsion-free Abelian groups of rank 2 using torsion-free groups of rank 1 are studied. Necessary and sufficient conditions are found under which a group given by such a representation is quotient divisible. A criterion is obtained for two p-minimal quotient divisible torsion-free groups of rank 2 to be isomorphic to each other. An example is constructed showing that two such groups can be embedded in each other but be nonisomorphic. A series of properties of fundamental systems of elements of quotient divisible groups of arbitrary finite rank is established.
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