A Nilpotent Quotient Algorithm for Certain Infinitely Presented Groups and its Applications

  title={A Nilpotent Quotient Algorithm for Certain Infinitely Presented Groups and its Applications},
  author={Laurent Bartholdi and Bettina Eick and Ren{\'e} Hartung},
  journal={Int. J. Algebra Comput.},
We describe a nilpotent quotient algorithm for a certain class of infinite presentations: the so-called finite L-presentations. We then exhibit finite L-presentations for various examples and report on the application of our nilpotent quotient algorithm to them. As a result, we obtain conjectural descriptions of the lower central series structure of various interesting groups including the Grigorchuk supergroup, the Brunner–Sidki–Vieira group, the Basilica group, certain generalizations of the… 

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