Brecht Verbeken

collaborators

20 papers

math.GR2026

Cyclic-by-abelian counterexamples to the second and third Zassenhaus conjectures

Brecht Verbeken

Let $r > 1$ with $g cd (r, 30) = 1$ . We construct a finite group $G_{r} = (C_{5} \times C_{3} \times C_{r}) ⋊ W$ , where $∣ W ∣ = 32$ and $G_{r}^{'} ≅ C_{60 r}$ , together with an augmentation-preservin…

math.GR2026

Powerful multiplicative groups do not force right nilpotence in finite braces

Brecht Verbeken

For every odd prime $p$ , we construct a finite left brace $A_{p}$ of order $p^{2 p + 1}$ whose additive group is elementary abelian and whose multiplicative group $G_{p}$ is a powerful $p…

math.GR2026

The N-Prime Graph Question is equivalent to the Prime Graph Question

Brecht Verbeken

Let $G$ be a finite group and let $V (Z G)$ be the group of normalized units of its integral group ring. We prove that every $N$ -prime arc of $V (Z G)$ either already o…

math.RA2026

The Type III realisation conjecture of Kirkland and Å migoc

Brecht Verbeken, Vincent Ginis

Kirkland and Å migoc constructed a family of stochastic matrices realising the Type III boundary polynomials in the KarpeleviÄ region and conjectured that, conversely, every stoch…

cs.CL2026

Thinking Like a Scientist? A Structural Study of LLM-Generated Research Methods

Francesca Carlon, Brecht Verbeken, Vincent Ginis +1

Large Language Models (LLMs) are increasingly used to guide research methodology, yet their default methodological tendencies under minimal prompting remain unclear. Here, we promp…

math.SP2026

On the Spectral Region of 4-Cycle Stochastic Matrices

Brando Vagenende, Brecht Verbeken, Andres Algaba +1

We study the spectrum of 4-cycle row-stochastic matrices. For real eigenvalues the spectral region is [-1,1]. For nonreal eigenvalues a+ib we derive necessary conditions in terms o…