Let $L/K$ be a finite Galois extension of p-adic fields with group G. It is well-known that ${\mathcal{O}}_L$ contains a free ${\mathcal{O}}_K[G]$-submodule of finite index. We study the minimal index of such a free submodule, and determine it exactly in several cases, including for any cyclic extension of degree p of p-adic fields.

中文翻译：

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p-adic 域的扩展距离具有正规积分基有多远？

让 $升/钾$是具有群G的p进场的有限伽罗瓦扩展。众所周知，${\mathcal{哦}}_{升}$ 包含一个免费的 ${\mathcal{哦}}_{钾}[G]$- 有限索引的子模块。我们研究了最小的这样一个自由子模块的指标，准确地确定它在一些情况下，包括度的任何循环扩展p的p进制领域。