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This post is basically a quantum extension of Is every finite group a group of “symmetries”? Here finite quantum group means finite dimensional Hopf ${\rm C}^{\star}$-algebra. Frucht's theorem ...

Let $G$ be a finite group and $D(G)$ its quantum double. Its finite dimensional complex representations are classified in this Dijkgraaf et al. Quasi-Quantum Groups Related To Orbifold Models. However,...

Let $G$ be a finite group and $D(G)$ its quantum double. As in my previous question, a typical irreducible representation (finite dimensional over $\mathbb{C}$) is labeled by $(\theta,\pi)$, where $\...

A cyclic number is a natural number $n$ such that any group of order $n$ is cyclic. A003277 Theorem (T. Szele, 1947): A number $n$ is cyclic if and only if it is coprime to its Euler totient $\varphi(...

Let $G$ be a group. For $g,h \in G$, let $[g,h]=g^{-1}h^{-1}gh$ be a commutator. The normal subgroup $G' = \langle [g,h] \ | \ g,h \in G \rangle$ is called the commutator subgroup or derived subgroup. ...