Lie rings related to the $p$-groups of maximal class

Bettina Eick; Patali Komma; Subhrajyoti Saha

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arXiv · 2512.14547

Lie rings related to the $p$-groups of maximal class

Bettina Eick·Patali Komma·Subhrajyoti Saha

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Abstract

The Lazard correspondence induces a close relation between the $p$-groups of maximal class and a certain type of Lie ring constructed from $p$-adic number fields. Our aim here is to investigate such Lie rings. In particular, we show that they are always finite. It then follows that they are nilpotent of small class. These results close an important gap in (Eick, Komma \& Saha 2025).

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Bettina Eick, Patali Komma, Subhrajyoti Saha. 2025-12-16. Lie rings related to the $p$-groups of maximal class. https://arxiv.org/abs/2512.14547

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