Nilpotent Lie rings of order 2^n

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Number of nilpotent Lie rings of small orders

Exponent n Value 2^n Number of Lie rings of order 2^n Reason/Explanation/List
0 1 1 trivial Lie ring
1 2 1 abelian Lie ring with additive group cyclic group:Z2.
2 4 2 abelian Lie rings with additive groups cyclic group:Z4 and Klein four-group respectively. See Lie rings of order 4, classification of Lie rings of prime-square order.
3 8 5 See nilpotent Lie rings of order 8, classification of nilpotent Lie rings of prime-cube order.
4 16  ? See nilpotent Lie rings of order 16.
5 32  ? See nilpotent Lie rings of order 32.