Abstract
We classify and count the nilpotent Lie rings of order p 8 with maximal class for p ≥ 5 . This also provides a classification of the groups of order p 8 with maximal class for p ≥ 11 via the Lazard correspondence. We also record the number of nilpotent Lie rings/groups of order pn with maximal class for n ≤ 7 from currently known data and discuss its asymptotic behavior as n grows and its potential connection to Higman’s PORC conjecture.
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