Andreas Thom

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20242026

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math.GR2026

On prime endomorphisms of the free group of rank two

Andreas Thom

We study prime endomorphisms of the free group $F_{2}$ . The main results provide lower and upper bounds for the logarithmic density $δ_{np}$ of non-prime endomorphisms: $$ \…

math.GR2026

Unitary representations and von Neumann's continuous geometries

Friedrich Martin Schneider, Andreas Thom

We prove that the unit group of a non-discrete irreducible, continuous ring, in the sense of John von Neumann, does not admit any non-trivial unitary representation continuous with…

math.GR2025

The anabelian restricted Burnside problem

Andreas Thom

Let $n, d \in N$ and $w \in F_{n}$ be non-trivial. We prove that the relatively free group of rank $d$ in the variety defined by the group law $w$ has a largest anabel…

math.GR2024

On automorphism groups of metric reduced products of symmetric groups

Ben De Bondt, Andreas Thom

We study isomorphisms between metric reduced products of symmetric groups with the normalized Hamming metric assuming the open coloring axiom $OCA$ and Martin's axiom for…

math.GR2024

Quadratic maps between non-abelian groups

Asgar Jamneshan, Andreas Thom

Gowers and Hatami initiated the inverse theory for the uniformity norms $U^{k}$ of matrix-valued functions on non-abelian groups by proving a $1%$ -inverse theorem for the $U^{2}$ -norm…

math.GR2024

High-dimensional expansion and soficity of groups

Lukas Gohla, Andreas Thom

For $d \geq 4$ and $p$ a sufficiently large prime, we construct a lattice $Γ \leq PSp_{2 d} (Q_{p}),$ such that its universal central extension cannot be sofic if $Γ$ sati…