M. Loukaki

A simultaneous variant of the Hall-Paige theorem and applications

For $k\geq 1$ , we say that a finite group $G$ satisfies property $\mathcal P_k$ if, for every $\beta_1,\ldots,\beta_k\in\operatorname{Aut}(G)$, there exists a bijection $f$ of $G$ such that each map $g\mapsto \beta_i(g)f(g)$ is a bijection. For $k=1$ this is equivalent to the classical Hall--Paige complete mapping pro...