7 problems

Let $G_{m,n}$ be the metacyclic group … where $s$ has order $m$ modulo $n$. For a finite group $G$, the small Davenport constant $\mathsf d(G)$ is the maximal integer $\ell$ such t…

Bass's conjecture. The Davenport constant of $G_{a,b,g}$ is

Liftability conjecture. Every non-split metacyclic action on $S_g$ lifts under a suitably chosen finite regular cyclic cover to a split metacyclic action.

Let $G=G(m,n,k)$ be a finite metacyclic group with trivial centre, and let ${\rm P}(G)$ and $\Lambda(G)$ denote the left and right commutation semigroups, respectively. An orbit is…

Let $H_{n,m}$ denote the metacyclic group considered in the paper, with $n\geq 4$ and $m$ even. Write $\mathsf{s}(G)$ for the Erdős–Ginzburg–Ziv constant of a finite group $G$, the…

Let $p$ be an odd prime, let $k$ be a primitive $(p-1)$-st root of $1$ modulo $p$, and suppose that $K(r)$ is a $2$-bridge knot with $\Delta_{K(r)}(k)\equiv0\pmod p$. Let…

Let $K$ be a knot whose knot group $G(K)$ maps onto the non-abelian semidirect product … where $p$ is an odd prime and $k$ is a primitive $m$-th root of $1$ modulo $p$. Let…