11 citations · 24 across the 12 of their papers we have counts for
14 papers
Block mapping class groups and their finiteness properties
Javier Aramayona, Julio Aroca, María Cumplido +2
A Cantor surface is a non-compact surface obtained by gluing copies of a fixed compact surface (a block), with boundary components, in a tree-like fashio…
Type systems and maximal subgroups of Thompson's group
James Belk, Collin Bleak, Martyn Quick +1
We introduce the concept of a type system~$\Part$, that is, a partition on the set of finite words over the alphabet~ compatible with the partial action of Thompson's grou…
Thompson's group is -generated
Collin Bleak, Scott Harper, Rachel Skipper
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…
Braiding groups of automorphisms and almost-automorphisms of trees
Rachel Skipper, Matthew C. B. Zaremsky
We introduce "braided" versions of self-similar groups and Röver--Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the f…
A new construction of subgroups of big mapping class groups
Carolyn R. Abbott, Hannah Hoganson, Marissa Loving +2
We explicitly construct new subgroups of the mapping class groups of an uncountable collection of infinite-type surfaces, including, but not limited to, free groups, Baumslag-Solit…
Homological stability for the ribbon Higman--Thompson groups
Rachel Skipper, Xiaolei Wu
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 th…
Finiteness properties for relatives of braided Higman--Thompson groups
Rachel Skipper, Xiaolei Wu
We study the finiteness properties of the braided Higman--Thompson group with labels in , and and with labels in w…
Commensurability growth of branch groups
Khalid Bou-Rabee, Rachel Skipper, Daniel Studenmund
Fixing a subgroup in a group , the commensurability growth function assigns to each the cardinality of the set of subgroups of with $[Γ: Γ\cap Δ][Δ: Γ\cap Δ] = n…
On the Cantor-Bendixson rank of the Grigorchuk group and the Gupta-Sidki group
Rachel Skipper, Phillip Wesolek
We study the Cantor--Bendixson rank of the space of subgroups for members of a general class of finitely generated self-replicating branch groups. In particular, we show for ei…
Lamplighter groups, bireversible automata and rational series over finite rings
Rachel Skipper, Benjamin Steinberg
We realize lamplighter groups , with a finite abelian group, as automaton groups via affine transformations of power series rings with coefficients in a finite…
Simple groups separated by finiteness properties
Rachel Skipper, Stefan Witzel, Matthew C. B. Zaremsky
We show that for every positive integer there exists a simple group that is of type but not of type . For these groups are the first k…
The congruence subgroup problem for a family of branch groups
Rachel Skipper
We construct a family of groups which generalize the Hanoi towers group and study the congruence subgroup problem for the groups in this family. We show that unlike the Hanoi tower…
Almost-automorphisms of trees, cloning systems and finiteness properties
Rachel Skipper, Matthew C. B. Zaremsky
We prove that the group of almost-automorphisms of the infinite rooted regular -ary tree arises naturally as the Thompson-like group of a so called -ary cloni…
A constructive proof that the Hanoi towers group has non-trivial rigid kernel
Rachel Skipper
In 2012, Bartholdi, Siegenthaler, and Zalesskii computed the rigid kernel of the Hanoi towers group. We present a simpler proof that the rigid kernel is the Klein 4 group. In the c…