Origins
Pure subgroups are also called isolated subgroups or serving subgroups and were first investigated in Prüfer's 1923 paper which described conditions for the decomposition of primary abelian groups as direct sums of cyclic groups using pure subgroups. The work of Prüfer was complemented by Kulikoff where many results were proved again using pure subgroups systematically. In particular, a proof was given that pure subgroups of finite exponent are direct summands. A more complete discussion of pure subgroups, their relation to infinite abelian group theory, and a survey of their literature is given in Irving Kaplansky's little red book.
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