|ISSN 1088-6826(online) ISSN 0002-9939(print)|
A note on torsion-free abelian groups of finite rank
Abstract: Let be a torsion-free abelian group of rank and a maximal set of rationally independent elements in . It is well known that any can be uniquely written , for some , the rational numbers. This enables us to define, for any such , a collection of sub-groups of and ``natural'' isomorphisms, denoted by . It is known that if is of rank two, then may be recovered from is a natural way. The following result is obtained for groups of rank greater than two:
Theorem. Let be torsion free abelian groups of finite rank with for suitable . Let be the free subgroups of generated by . Then .
An additional condition is given for pairs ( such that implies .
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