Hall-Paige conjecture

This article is about a conjecture in the following area in/related to group theory: finite groups. View all conjectures and open problems

Statement

Suppose $G$ is a finite group with the property that every $2$-Sylow subgroup of $G$ is either trivial or non-cyclic. Then, there exists a complete map from $G$ to $G$: a bijection $\varphi :G\to G$ such that the map $g\mapsto g\varphi (g)$ is also a bijection.

Related conjectures

• Snevily's conjecture