6 papers
Commutative decomposition of infinite symmetric groups and transformation monoids
Luna Elliott, Alex Levine
The commutative subgroup width of a group is the smallest such that there are abelian subgroups with . Commutative (i…
Counting automorphic orbits in finitely generated groups
Luna Elliott, Alex Evetts, Alex Levine
We study an analogue of the conjugacy growth function in finitely generated groups: the automorphic growth function. This counts the number of automorphic orbits that intersect the…
The Diophantine problem in Thompson's group F
Luna Elliott, Alex Levine
We show that the Diophantine problem in Thompson's group F is undecidable. Our proof uses the facts that F has finite commutator width and rank 2 abelianisation, then uses similar…
Computing congruences of finite inverse semigroups
Luna Elliott, Alex Levine, James D. Mitchell
In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from…
Classifying the Polish semigroup topologies on the symmetric inverse monoid
Serhii Bardyla, Luna Elliott, James Mitchell +1
We classify all Polish semigroup topologies on the symmetric inverse monoid on the natural numbers. This result answers a question of Elliott et al. There are countably infinitely…
E-disjunctive inverse semigroups
Luna Elliott, Alex Levine, James Mitchell
In this paper we provide an overview of the class of inverse semigroups such that every congruence on relates at least one idempotent to a non-idempotent; such inverse semi…