The wreath product of $\mathbb {Z}$ with $\mathbb {Z}$ has Hilbert compression exponent $\frac {2}{3}$
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چکیده
منابع مشابه
The wreath product of Z with Z has Hilbert compression exponent 23
Let G be a finitely generated group, equipped with the word metric d associated with some finite set of generators. The Hilbert compression exponent of G is the supremum over all α ≥ 0 such that there exists a Lipschitz mapping f : G → L2 and a constant c > 0 such that for all x, y ∈ G we have ‖ f (x) − f (y)‖2 ≥ cd(x, y). In [2] it was shown that the Hilbert compression exponent of the wreath ...
متن کامل1 6 Ju n 20 07 The wreath product of Z with Z has Hilbert compression exponent 23
Let G be a finitely generated group, equipped with the word metric d associated with some finite set of generators. The Hilbert compression exponent of G is the supremum over all α ≥ 0 such that there exists a Lipschitz mapping f : G → L2 and two constants c1, c2 > 0 such that for all x, y ∈ G we have ‖ f (x)− f (y)‖2 ≥ c1d(x, y)− c2. Tessara [16] proved that the Hilbert compression exponent of...
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For a nite group G the commutativity degree denote by d(G) and dend:$$d(G) =frac{|{(x; y)|x, yin G,xy = yx}|}{|G|^2}.$$ In [2] authors found commutativity degree for some groups,in this paper we nd commutativity degree for a class of groups that have high nilpontencies.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09501-4