Isoperimetric functions of nilpotent groups amalgamated along a cyclic subgroup (Q2716946)
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scientific article; zbMATH DE number 1599656
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isoperimetric functions of nilpotent groups amalgamated along a cyclic subgroup |
scientific article; zbMATH DE number 1599656 |
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Isoperimetric functions of nilpotent groups amalgamated along a cyclic subgroup (English)
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15 January 2002
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amalgams of groups
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torsionfree nilpotent groups
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isoperimetric functions
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It is shown that amalgams of finitely generated torsionfree nilpotent groups of class \(\leq c\) along a cyclic subgroup satisfy a polynomial isoperimetric inequality of degree at most \(4c^2\). It is proved that the distorsion of the amalgamated subgroup is bounded above by a polynomial of degree \(c\). An example of a non-cyclic amalgam of finitely generated torsionfree nilpotent groups along an Abelian, isolated and normal subgroup having an exponential isoperimetric inequality is given.
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