6 problems

Szép's conjecture. No non-abelian finite simple group $G$ has a factorisation of the form

Let $G$ be a finite non-abelian group. A factorization of $G$ is a tuple of subsets whose product represents every element of $G$ uniquely. A factor has simple order or order $4$ w…

Let $G$ be a finite group and let $|G|=ab$ be a factorization of its order. A factorization $G=AB$ is direct when every element of $AB$ has a unique representation $x=ab$ with…

Let $G$ be a finite group. A factorization of $G$ is an expression $G=A_1\ldots A_k$ with $|G|=|A_1|\cdots|A_k|$, so every element of $G$ has a unique representation as…

Complete splitting conjecture. Then

Let $G$ be a finite group with prime factorization … A logarithmic signature for $G$ is an ordered tuple of subsets that gives every element of $G$ a unique product decomposition,…