We extend the theory of countably generated Demushkin groups to Demushkin groups of arbitrary rank. We investigate their algebraic properties and invariants, count their isomorphism classes, and study their realization as absolute Galois group. At the end, we compute their profinite completion and conclude with some results on profinite completion of absolute Galois groups.

中文翻译：

---

无数等级的德穆什金团体

我们将可数生成的 Demushkin 群理论扩展到任意阶的 Demushkin 群。我们研究它们的代数性质和不变量，计算它们的同构类，并研究它们作为绝对伽罗瓦群的实现。最后，我们计算它们的有限完备性，并得出绝对伽罗瓦群的有限完备性的一些结果。