3 problems

Let $G$ be a finite group of order $n$, let $C_n$ denote the cyclic group of order $n$, and let $N(a,G)$ be the number of connected components of the functional graph $G(a,G)$ asso…

Subbarao–Fabrykowski conjecture. If $T_f$ is infinite, then either $f(n)=0$ for every $n\in\mathbb{N}$ or $f$ is a global power map, meaning $f(n)=n^k$ for some…

Let $f:\mathbb{Q}\longrightarrow\mathbb{Q}$. For each prime $p$, define … where $\mathbb{Z}_{(p)}^\times$ is the group of elements of $\mathbb{Q}$ whose numerator and denominator a…