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Equivalent Abelian Groups

Published online by Cambridge University Press:  20 November 2018

J. De Groot
J. De Groot*
Affiliation:
Mathematisch Instituut University of Amsterdam
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Throughout this note all groups are abelian, written additively. We refer to Kurosh (8; 9) for notation, terminology and theorems used without reference. We recall the notion of a serving subgroup (or pure subgroup) of a group . This is a subgroup in which for every natural number n every equation nx = s, s ∊ can be solved provided that it can be solved in . If is torsion-free, “linearly closed” subgroups coincide with serving subgroups and is a serving subgroup if and only if / is torsionfree.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 291 - 297
Copyright
Copyright © Canadian Mathematical Society 1957

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