12 citations · 18 across the 7 of their papers we have counts for
9 papers
Uncountably many local isomorphism types of compactly generated simple groups
Ilaria Castellano, Jorge Fariña-Asategui, Mikel Eguzki Garciarena +7
A major open question in the theory of locally compact groups is the following. Let be the class of non-discrete compactly generated totally disconnected locally comp…
The structure of groups with all proper quotients virtually nilpotent
Benjamin Klopsch, Martyn Quick
Just infinite groups play a significant role in profinite group theory. For each , we consider more generally JNNF profinite (or, in places, discrete) groups that are…
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…
On separability properties in direct products of semigroups
Gerard O'Reilly, Martyn Quick, Nik Ruskuc
We investigate four finiteness conditions related to residual finiteness: complete separability, strong subsemigroup separability, weak subsemigroup separability and monogenic subs…
On separability finiteness conditions in semigroups
Craig Miller, Gerard O'Reilly, Martyn Quick +1
Taking residual finiteness as a starting point, we consider three related finiteness properties: weak subsemigroup separability, strong subsemigroup separability and complete separ…
Permutation-based presentations for Brin's higher-dimensional Thompson groups
Martyn Quick
The higher-dimensional Thompson groups , for , were introduced by Brin in 2005. We provide new presentations for each of these infinite simple groups. The first is an…
Automorphism groups of linearly ordered structures and endomorphisms of the ordered set of rational numbers
Jillian D. McPhee, James D. Mitchell, Martyn Quick
We investigate the structure of the monoid of endomorphisms of the ordered set of rational numbers. We show that for any countable linearly ordered set , t…
The infinite simple group V of Richard J. Thompson: presentations by permutations
Collin Bleak, Martyn Quick
We show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group , known by Thompson to have a presentation with four generators and fo…
Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph
Igor Dolinka, Robert D. Gray, Jillian D. McPhee +2
We establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph . As a consequence we show that, for any countable graph…