The groups and nilpotent Lie rings of order $p^8$ with maximal class

TL;DR

This paper classifies nilpotent Lie rings of order p^8 with maximal class for primes p ≥ 5, and also classifies groups of order p^8 with maximal class for p ≥ 11 using the Lazard correspondence.

Contribution

It provides the first complete classification of these algebraic structures of order p^8 with maximal class for specified primes.

Findings

Classification of nilpotent Lie rings of order p^8 with maximal class for p ≥ 5.

Classification of groups of order p^8 with maximal class for p ≥ 11.

Application of Lazard correspondence to relate Lie rings and groups.

Abstract

We classify the nilpotent Lie rings of order $p^8$ with maximal class for $p \ge 5$. This also provides a classification of the groups of order $p^8$ with maximal class for $p \ge 11$ via the Lazard correspondence.