4 problems

Let $G$ and $H$ be finite $2$-groups of the same order. A construction preserves exactly three quarters of the corresponding multiplication tables when the tables agree in exactly…

Multiplication-table lattice value conjecture. For $n \geq 2$,

Brent–Kung conjecture. The asymptotic behaviour of $M(N)$ satisfies

Multiplication-table dichotomy conjecture. If $u-L\log_2 y\to+\infty$, which implies