Localization of profinite groups
The authors study the concept of \(\pi\)-local groups and \(\pi\)- localization for profinite groups. It turns out that a profinite group G is \(\pi\)-local if and only if it is a \(\pi\)-group. The main interest then lies on the question whether and how one can construct a profinite group G from its \(\pi\)-localizations \(G_{\pi}\) for \(\pi\) in a given family \(\Pi\) of sets of primes. For a partition \(\Pi\) of the set \({\mathfrak P}\) of all primes this can be done exactly for the direct products of \(\pi\)- groups, \(\pi \in \Pi\). Finally the localizations in the categories of profinite and of abstract groups are compared and sufficient conditions are given under which both coincide.
scientific article; zbMATH DE number 3865564