Residually free groups do not admit a uniform polynomial isoperimetric function

Claudio Llosa Isenrich; Romain Tessera

doi:10.1090/proc/15082

Residually free groups do not admit a uniform polynomial isoperimetric function

Claudio Llosa Isenrich
, Romain Tessera

University of Vienna
Université Paris Cité

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Résumé

We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups by producing a sequence of subgroups G_r ≤ F₂⁽¹⁾ × ··· × F₂⁽r⁾ of direct products of 2-generated free groups with Dehn functions bounded below by n^r. The groups G_r are obtained from the examples of non-coabelian subdirect products of free groups constructed by Bridson, Howie, Miller, and Short. As a consequence we obtain that residually free groups do not admit a uniform polynomial isoperimetric function.

langue originale	Anglais
Pages (de - à)	4203-4212
Nombre de pages	10
journal	Proceedings of the American Mathematical Society
Volume	148
Numéro de publication	10
Les DOIs	https://doi.org/10.1090/proc/15082
état	Publié - 1 oct. 2020
Modification externe	Oui

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10.1090/proc/15082

Contient cette citation

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abstract = "We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups by producing a sequence of subgroups Gr ≤ F2(1) × ··· × F2(r) of direct products of 2-generated free groups with Dehn functions bounded below by nr. The groups Gr are obtained from the examples of non-coabelian subdirect products of free groups constructed by Bridson, Howie, Miller, and Short. As a consequence we obtain that residually free groups do not admit a uniform polynomial isoperimetric function.",

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N2 - We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups by producing a sequence of subgroups Gr ≤ F2(1) × ··· × F2(r) of direct products of 2-generated free groups with Dehn functions bounded below by nr. The groups Gr are obtained from the examples of non-coabelian subdirect products of free groups constructed by Bridson, Howie, Miller, and Short. As a consequence we obtain that residually free groups do not admit a uniform polynomial isoperimetric function.

AB - We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups by producing a sequence of subgroups Gr ≤ F2(1) × ··· × F2(r) of direct products of 2-generated free groups with Dehn functions bounded below by nr. The groups Gr are obtained from the examples of non-coabelian subdirect products of free groups constructed by Bridson, Howie, Miller, and Short. As a consequence we obtain that residually free groups do not admit a uniform polynomial isoperimetric function.

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Residually free groups do not admit a uniform polynomial isoperimetric function

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