ترغب بنشر مسار تعليمي؟ اضغط هنا

Dehn Function of Finitely Presented Metabelian Groups

143   0   0.0 ( 0 )
 نشر من قبل Wenhao Wang
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف Wenhao Wang




اسأل ChatGPT حول البحث

In this paper, we compute an upper bound for the Dehn function of a finitely presented metabelian group. In addition, we prove that the same upper bound works for the relative Dehn function of a finitely generated metabelian group. We also show that every wreath product of a free abelian group of finite rank with a finitely generated abelian group can be embedded into a metabelian group with exponential Dehn function.

قيم البحث

اقرأ أيضاً

172 - Mark Sapir 2018
The isoperimeric spectrum consists of all real positive numbers $alpha$ such that $O(n^alpha)$ is the Dehn function of a finitely presented group. In this note we show how a recent result of Olshanskii completes the description of the isoperimetric s pectrum modulo the celebrated Computer Science conjecture (and one of the seven Millennium Problems) $mathbf{P=NP}$ and even a formally weaker conjecture.
We prove that all invariant random subgroups of the lamplighter group $L$ are co-sofic. It follows that $L$ is permutation stable, providing an example of an infinitely presented such a group. Our proof applies more generally to all permutational wre ath products of finitely generated abelian groups. We rely on the pointwise ergodic theorem for amenable groups.
The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups $G$ with the following properties: (i) $G$ is finitely generated, (ii) $G$ is amenable , e.g. of intermediate growth, (iii) any finitely presented group $E$ with a quotient isomorphic to $G$ contains non-abelian free subgroups, or the stronger (iii) any finitely presented group with a quotient isomorphic to $G$ is large.
We propose a numerical method for studying the cogrowth of finitely presented groups. To validate our numerical results we compare them against the corresponding data from groups whose cogrowth series are known exactly. Further, we add to the set of such groups by finding the cogrowth series for Baumslag-Solitar groups $mathrm{BS}(N,N) = < a,b | a^N b = b a^N >$ and prove that their cogrowth rates are algebraic numbers.
We exhibit explicit infinite families of finitely presented, Kazhdan, simple groups that are pairwise not measure equivalent. These groups are lattices acting on products of buildings. We obtain the result by studying vanishing and non-vanishing of their $L^2$-Betti numbers.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا