Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Skipper, Rachel"'
We provide a family of generating sets $S_{\alpha}$ of the Higman--Thompson groups $V_n$ that are parametrized by certain sequences $\alpha$ of elements in $V_n$. These generating sets consist of $3$ involutions $\sigma$, $\tau$, and $s_{\alpha}$, wh
Externí odkaz:
http://arxiv.org/abs/2411.09069
We show that R. Thompson's group $T$ is a maximal subgroup of the group $V$. The argument provides examples of foundational calculations which arise when expressing elements of $V$ as products of transpositions of basic clopen sets in Cantor space $\
Externí odkaz:
http://arxiv.org/abs/2409.12621
Autor:
Aramayona, Javier, De Pool, Rodrigo, Skipper, Rachel, Tao, Jing, Vlamis, Nicholas G., Wu, Xiaolei
We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomorphisms. This class of subgroups includes the pure mapping class group
Externí odkaz:
http://arxiv.org/abs/2409.05502
We consider analogues of Grigorchuk-Gupta-Sidki (GGS-)groups acting on trees of growing degree; the so-called growing GGS-groups. These groups are not just infinite and do not possess the congruence subgroup property, but many of them are branch and
Externí odkaz:
http://arxiv.org/abs/2405.20961
A Cantor surface $\mathcal C_d$ is a non-compact surface obtained by gluing copies of a fixed compact surface $Y^d$ (a block), with $d+1$ boundary components, in a tree-like fashion. For a fixed subgroup $H
Externí odkaz:
http://arxiv.org/abs/2207.06671
We introduce the concept of a type system~$\Part$, that is, a partition on the set of finite words over the alphabet~$\{0,1\}$ compatible with the partial action of Thompson's group~$V$, and associate a subgroup~$\Stab{V}{\Part}$ of~$V$. We classify
Externí odkaz:
http://arxiv.org/abs/2206.12631
Every finite simple group can be generated by two elements and, in fact, every nontrivial element is contained in a generating pair. Groups with this property are said to be $\frac{3}{2}$-generated, and the finite $\frac{3}{2}$-generated groups were
Externí odkaz:
http://arxiv.org/abs/2206.05316
Publikováno v:
Can. J. Math.-J. Can. Math. 76 (2024) 555-593
We introduce "braided" versions of self-similar groups and R\"over--Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the first author and Wu, who considered the case when the self-similar gr
Externí odkaz:
http://arxiv.org/abs/2109.13389
We explicitly construct new subgroups of the mapping class groups of an uncountable collection of infinite-type surfaces, including, but not limited to, right-angled Artin groups, free groups, Baumslag-Solitar groups, mapping class groups of other su
Externí odkaz:
http://arxiv.org/abs/2109.05976
Autor:
Skipper, Rachel, Wu, Xiaolei
We generalize the notion of asymptotic mapping class groups and allow them to surject to the Higman--Thompson groups, answering a question of Aramayona and Vlamis in the case of the Higman--Thompson groups. When the underlying surface is a disk, thes
Externí odkaz:
http://arxiv.org/abs/2106.08751