On the Cantor-Bendixson rank of metabelian groups

Cornulier, Yves

Annales de l'Institut Fourier, Tome 61 (2011) no. 2, pp. 593-618.

On étudie le rang de Cantor-Bendixson des groupes métabéliens ou virtuellement métabéliens dans l’espace des groupes marqués, et on exhibe notamment une suite $\left(G_n\right)$ de groupes virtuellement métabéliens de présentation finie à deux générateurs, de rang de Cantor-Bendixson égal à ${\omega }^n$.

We study the Cantor-Bendixson rank of metabelian and virtually metabelian groups in the space of marked groups, and in particular, we exhibit a sequence $\left(G_n\right)$ of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank ${\omega }^n$.

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