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.
Yves de Cornulier 1 ; Romain Tessera 1
@article{CML_2010__2_4_431_0,
author = {Yves de~Cornulier and Romain Tessera},
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 = {https://cml.centre-mersenne.org/articles/10.1142/S1793744210000235/}
}
TY - JOUR AU - Yves de Cornulier AU - Romain Tessera 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 - https://cml.centre-mersenne.org/articles/10.1142/S1793744210000235/ DO - 10.1142/S1793744210000235 LA - en ID - CML_2010__2_4_431_0 ER -
%0 Journal Article %A Yves de Cornulier %A Romain Tessera %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 https://cml.centre-mersenne.org/articles/10.1142/S1793744210000235/ %R 10.1142/S1793744210000235 %G en %F CML_2010__2_4_431_0
Yves de Cornulier; Romain Tessera. Metabelian groups with quadratic Dehn function and Baumslag–Solitar groups. Confluentes Mathematici, Tome 2 (2010) no. 4, pp. 431-443. doi : 10.1142/S1793744210000235. https://cml.centre-mersenne.org/articles/10.1142/S1793744210000235/
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