Alex Levine

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20242026

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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…