Non-associative Gröbner bases, finitely-presented Lie rings and the Engel condition, II

@article{Cical2009NonassociativeGB,
  title={Non-associative Gr{\"o}bner bases, finitely-presented Lie rings and the Engel condition, II},
  author={Serena Cical{\`o} and Willem A. de Graaf},
  journal={J. Symb. Comput.},
  year={2009},
  volume={44},
  pages={786-800}
}
We give an algorithm for constructing a basis and a multiplication table of a finite-dimensional finitely-presented Lie ring. Secondly, we give relations that are equivalent to the n-Engel condition, and only have to be checked for the elements of a basis of a Lie ring. We apply this to construct the freest t-generator Lie rings that satisfy the n-Engel condition, for (t,n)=(2,3),(3,3),(4,3),(2,4). 

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