5 problems

Let $r \geq 2$ and $c \geq 3$ be integers. The Reidemeister spectrum of a group is the set of finite Reidemeister numbers of its automorphisms, together with $\infty$ when an autom…

For a finite group $G$, let $k(G)$ denote its class number. A finite group has full extended Reidemeister spectrum when its extended Reidemeister spectrum contains every possible v…

Fel'shtyn–Tertooy conjecture. Every finitely generated, residually finite group without the $R_\infty$ property is virtually solvable.

Let $N_{r,c}$ be a free nilpotent group with rank $r\geq 2$ and nilpotency class $c>2$. The Reidemeister spectrum $\operatorname{Spec}_R(N_{r,c})$ is the set of finite Reidemeister…

Let $m\geq 2$ and $n\in\mathbb{N}$. Consider the polynomial … Writing $R_2$ for the second Reidemeister-number factor associated with this polynomial, the even-degree polynomial co…