The Nottingham group is the unique Sylow pro‐ $p$ subgroup of the automorphism group of the formal power series algebra over a finite field. This group has been intensively studied in the last decades for its interesting properties, just infiniteness being one of the most remarkable. Shalev and Leedham‐Green introduced the generalized Nottingham groups and confirmed that they are just infinite, however the proof was lost. Here we prove that the generalized Nottingham groups over finite fields of odd characteristic are hereditarily just infinite.

中文翻译：

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广义诺丁汉群的无限性

诺丁汉集团是独特的Sylow pro- $p$有限域上形式幂级数代数的自同构群的子群。在过去的几十年中，该小组对其有趣的性质进行了深入的研究，只是无限性是最杰出的性质之一。Shalev和Leedham-Green引入了广义的诺丁汉群，并确认它们只是无限的，但是证明丢失了。在这里，我们证明了具有奇特征的有限域上的广义诺丁汉群在遗传上只是无限的。