4 problems

Let $k$ be a fixed positive integer and let $G$ be a finite group. Suppose that at least half of the elements of $G$ have order $k$. Deaconescu's conjecture. Then $G$ is soluble. T…

Supersolvability conjecture. If

Nilpotent-group conjecture. One has

Let $G$ be a finite group of order $n$, let $C_n$ be the cyclic group of order $n$, and write $o(x)$ for the order of an element $x$. Element-order divisibility matching conjecture…