We prove that metabelian locally compact groups in a certain class have quadratic Dehn function. As an application, we embed the solvable Baumslag–Solitar groups in finitely presented metabelian groups with quadratic Dehn function. Also, we prove that Baumslag's finitely presented metabelian groups, in which the lamplighter groups embed, have quadratic Dehn function.
@article{CML_2010__2_4_431_0,
author = {de~Cornulier, Yves and Tessera, Romain},
title = {Metabelian groups with quadratic {Dehn} function and {Baumslag{\textendash}Solitar} groups},
journal = {Confluentes Mathematici},
pages = {431--443},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {2},
number = {4},
year = {2010},
doi = {10.1142/S1793744210000235},
language = {en},
url = {http://archive.numdam.org/articles/10.1142/S1793744210000235/}
}
TY - JOUR AU - de Cornulier, Yves AU - Tessera, Romain TI - Metabelian groups with quadratic Dehn function and Baumslag–Solitar groups JO - Confluentes Mathematici PY - 2010 SP - 431 EP - 443 VL - 2 IS - 4 PB - World Scientific Publishing Co Pte Ltd UR - http://archive.numdam.org/articles/10.1142/S1793744210000235/ DO - 10.1142/S1793744210000235 LA - en ID - CML_2010__2_4_431_0 ER -
%0 Journal Article %A de Cornulier, Yves %A Tessera, Romain %T Metabelian groups with quadratic Dehn function and Baumslag–Solitar groups %J Confluentes Mathematici %D 2010 %P 431-443 %V 2 %N 4 %I World Scientific Publishing Co Pte Ltd %U http://archive.numdam.org/articles/10.1142/S1793744210000235/ %R 10.1142/S1793744210000235 %G en %F CML_2010__2_4_431_0
de Cornulier, Yves; Tessera, Romain. Metabelian groups with quadratic Dehn function and Baumslag–Solitar groups. Confluentes Mathematici, Tome 2 (2010) no. 4, pp. 431-443. doi : 10.1142/S1793744210000235. http://archive.numdam.org/articles/10.1142/S1793744210000235/
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