Let G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice \(\mathcal {L}(H)\) embeds in \(\mathcal {L}(G)\). It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

中文翻译：

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Abelian群的纯子群的晶格理论表征

令G为阿贝尔群。这篇简短论文的目的是通过仅查看子组晶格\（\ mathcal {L}（H）\）嵌入\（\ mathcal {L}（G）的方式来描述一种识别G的纯子组 H的方法。\）。值得一提的是，所有结果均在纯净度通用定义的局部零能环境中进行。