Asymptotic property C of the wreath product Z ≀ Z \mathbb Z \wr \mathbb Z Z ≀ Z

[摘要] Using the relationship between transfinite asymptotic dimension and asymptotic property C, we obtain that the wreath product Z≀Z\mathbb Z \wr\mathbb ZZ≀Z has asymptotic property C. Specifically, we prove that the transfinite asymptotic dimension of the wreath product Z≀Z\mathbb Z \wr\mathbb ZZ≀Z does not exceed ω+1\omega+1ω+1.

[学科分类] 神经科学

[关键词] Wreath product;transfinite asymptotic dimension;asymptotic property C