On the geometry of free nilpotent groups
Abstract
In this article, we study geometric properties of nilpotent groups. We find a geometric criterion for the word problem for the finitely generated free nilpotent groups. By geometric criterion, we mean a way to determine whether two words represent the same element in a free nilpotent group of rank r and class k by analyzing their behavior on the Cayley graph of the free nilpotent group of rank r and class k-1.
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