7 problems

Zassenhaus conjecture. If $u\in\mathcal{U}(\mathbb ZG)$ is a unit of finite order, then $u$ is conjugate within $\mathbb QG$ to $\pm g$ for some $g\in G$.

Hertweck's blockwise isomorphism conjecture. For every $e\in\operatorname{PCI}({\mathbb Q}G)$,

Blockwise Spectrum Problem. For every primitive central idempotent $e\in\operatorname{PCI}({\mathbb Q}G)$,

Jespers–Sun's conjecture. A finite group $G$ has ND if and only if $\mathbb{Q}G$ has at most one matrix component.

Let $G$ be a finite group. Write $\mathbb{Z}G$ for its integral group ring and … for the group of normalized units, where $\varepsilon$ is the augmentation map. First Zassenhaus co…

Zassenhaus's order conjecture. There exists an element $g\in G$ such that

Let $G$ be a finite group. Write $\#(G)$ for the set of primes dividing the order of $G$. The Gruenberg–Kegel graph, or prime graph, of $G$ is the graph $\pi(G)$ whose vertices are…