Year: 2026
Type: preprint
Abstract: For $k\geq 1$ , we say that a finite group $G$ satisfies property $\mathcal P_k$ if, for every $β_1,\ldots,β_k\in\operatorname{Aut}(G)$, there exists a bijection $f$ of $G$ such that each map $g\mapsto β_i(g)f(g)$ is a bijection. For $k=1$ this is equivalent to the classical Hall--Paige complete mapping property. We prove that if $p$ is the smallest prime divisor of $|G|$, then $G$ satisfies $\mathcal P_k$ for every $k
Source: arXiv (Cornell University)
Author: Loukaki, Maria
Institution: University of Crete
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222504279