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Equivalent Abelian Groups
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1957
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