Title: Polynomial isoperimetric inequality for groups with function Δ(n) bounded by n(13−ε)
Abstract: We show that a polynomial isoperimetric inequality is true in ‘almost every group’, in some sense. Namely, we consider the function Δ(n),n∈Z,n>0, introduced, for a finitely generated group, by Robert Gilman, who proved that, for any group, Δ(n)⩽⌈n/3⌉, and that a slightly stricter condition Δ(n)<⌈n/3⌉ implies that the group is finitely presented and satisfies exponential isoperimetric inequality. In this paper, we show that the asymptotic condition Δ(n)⩽n(13−ε), where ε>0 is arbitrarily small but fixed, implies polynomial isoperimetric inequality.
Publication Year: 2004
Publication Date: 2004-03-01
Language: en
Type: article
Indexed In: ['crossref']
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