Alex Levine

collaborators

5 papers

math.GR2026

Commutative decomposition of infinite symmetric groups and transformation monoids

Luna Elliott, Alex Levine

The commutative subgroup width of a group $G$ is the smallest $k$ such that there are abelian subgroups $A_{0}, A_{1}, \dots, A_{k - 1} \leq G$ with $G = A_{0} A_{1} \dots A_{k - 1}$ . Commutative (i…

math.GR2026

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…

math.GR2025

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…

math.GR2025

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…

math.GR2025

E-disjunctive inverse semigroups

Luna Elliott, Alex Levine, James Mitchell

In this paper we provide an overview of the class of inverse semigroups $S$ such that every congruence on $S$ relates at least one idempotent to a non-idempotent; such inverse semi…