Elisha Falbel ; Pierre-Vincent Koseleff - The Number of Sides of a Parallelogram

dmtcs:251 - Discrete Mathematics & Theoretical Computer Science, January 1, 1999, Vol. 3 no. 2 - https://doi.org/10.46298/dmtcs.251
The Number of Sides of a Parallelogram

Authors: Elisha Falbel 1; Pierre-Vincent Koseleff ORCID-iD1

  • 1 Institut de Mathématiques de Jussieu

We define parallelograms of base a and b in a group. They appear as minimal relators in a presentation of a subgroup with generators a and b. In a Lie group they are realized as closed polygonal lines, with sides being orbits of left-invariant vector fields. We estimate the number of sides of parallelograms in a free nilpotent group and point out a relation to the rank of rational series.

Volume: Vol. 3 no. 2
Published on: January 1, 1999
Imported on: March 26, 2015
Keywords: Lie algebras,free group,Magnus group,lower central series,Lyndon basis,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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