Martin van Beek

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20242026

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math.GR2026

Fusion systems related to polynomial representations of $SL_{2} (q)$

Valentina Grazian, Chris Parker, Jason Semeraro +1

Let $q$ be a power of a fixed prime $p$ . We classify up to isomorphism all simple saturated fusion systems on a certain class of $p$ -groups constructed from the polynomial represen…

math.GR2025

Groups with conjugacy classes of coprime sizes

Rachel D. Camina, Attila MarÃ³ti, Emanuele Pacifici +6

Suppose that $x$ , $y$ are elements of a finite group $G$ lying in conjugacy classes of coprime sizes. We prove that $⟨ x^{G} ⟩ \cap ⟨ y^{G} ⟩$ is an abelian nor…

math.GR2024

Fusion Systems and Simple Groups With Class Two Sylow $p$ -subgroups

Martin van Beek

We determine all reduced saturated fusion systems supported on a finite $p$ -group of nilpotency class two. As a consequence, we obtain a new proof of Gilman & Gorenstein's classifi…

Fusion systems related to polynomial representations of SL2​(q)

Groups with conjugacy classes of coprime sizes

Fusion Systems and Simple Groups With Class Two Sylow p-subgroups

Fusion systems related to polynomial representations of $SL_{2} (q)$

Fusion Systems and Simple Groups With Class Two Sylow $p$ -subgroups