Discrete Mathematics & Theoretical Computer Science, Vol 3, No 2 (1999)

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DMTCS vol 3 no 2 (1999), pp. 33-42

Discrete Mathematics & Theoretical Computer Science


Volume 3 n° 2 (1999), pp. 33-42

author:Elisha Falbel and Pierre-Vincent Koseleff
title:The Number of Sides of a Parallelogram
keywords:Lie algebras, free group, Magnus group, lower central series, Lyndon basis
abstract: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.
reference: Elisha Falbel and Pierre-Vincent Koseleff (1999), The Number of Sides of a Parallelogram, Discrete Mathematics and Theoretical Computer Science 3, pp. 33-42
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Automatically produced on Thu Jan 21 10:14:11 MET 1999 by gustedt