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 of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank .
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 de groupes virtuellement métabéliens de présentation finie à deux générateurs, de rang de Cantor-Bendixson égal à .
Keywords: Metabelian groups, space of marked groups, Cantor-Bendixson analysis, Bieri-Strebel invariant, lattice of subgroups
Mot clés : groupes métabéliens, espace des groupes marqués, analyse de Cantor-Bendixson, invariant de Bieri-Strebel, treillis des sous-groupes
@article{AIF_2011__61_2_593_0, author = {Cornulier, Yves}, title = {On the {Cantor-Bendixson} rank of metabelian groups}, journal = {Annales de l'Institut Fourier}, pages = {593--618}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {2}, year = {2011}, doi = {10.5802/aif.2623}, zbl = {1238.20049}, mrnumber = {2895067}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2623/} }
TY - JOUR AU - Cornulier, Yves TI - On the Cantor-Bendixson rank of metabelian groups JO - Annales de l'Institut Fourier PY - 2011 SP - 593 EP - 618 VL - 61 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2623/ DO - 10.5802/aif.2623 LA - en ID - AIF_2011__61_2_593_0 ER -
%0 Journal Article %A Cornulier, Yves %T On the Cantor-Bendixson rank of metabelian groups %J Annales de l'Institut Fourier %D 2011 %P 593-618 %V 61 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2623/ %R 10.5802/aif.2623 %G en %F AIF_2011__61_2_593_0
Cornulier, Yves. On the Cantor-Bendixson rank of metabelian groups. Annales de l'Institut Fourier, Volume 61 (2011) no. 2, pp. 593-618. doi : 10.5802/aif.2623. http://www.numdam.org/articles/10.5802/aif.2623/
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