Author

Zhi-Lin Zhang

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Preprint Aug 2026

The $6\times6$ equality case of matrix spaces with rank-two commutators

Let $\mathcal V\subseteq M_6(\mathbb C)$ be a $17$-dimensional linear subspace such that $ \operatorname{rank}[S,T]\leq2 \quad(S,T\in\mathcal V). $ We prove that $\mathcal V$, or its transpose, is conjugate to the algebra $ \left\{ \begin{pmatrix} A&B&C\\ 0&\lambda I_2&D\\ 0&0&\lambda I_2 \end{pmatrix}: A,B,C,D\in M_2(...

Zhi-Lin Zhang · 1 citation

Preprint Aug 2026

Solubility from a disconnected common-divisor graph on $p$-regular conjugacy-class sizes

Let $G$ be a finite group and let $p$ be a prime. We prove that if the common-divisor graph on the nontrivial conjugacy-class sizes of $p$-regular elements of $G$ is disconnected, then $G$ is soluble, resolving the remaining case left by Camina, Mar\'{o}ti, Pacifici, Parker, Rekv\'{e}nyi, Saunders, Sotomayor, Tracey an...

Zhi-Lin Zhang · 0 citations