University of Isfahan International Journal of Group Theory 2251-7650 15 1 2025 07 13 Groups in which every Lagrange subset is a factor 43 48 29647 10.22108/ijgt.2025.144957.1957 EN Mohammad Hadi Hooshmand Department of Mathematics, Shi.C., Islamic Azad University, Shiraz, Iran Stefan Kohl Fridtjof-Nansen-Strasse 3, Rostock, Germany Journal Article 2025 04 18 We determine the finite groups $G$ in which every subset $A \subseteq G$ of cardinality dividing the order of $G$ is a <em>factor</em>, i.e. has a complement $B \subseteq G$ of cardinality $|G|/|A|$ such that $G = A \cdot B$ or $G = B \cdot A$. Finite group group factorization into subsets converse of Lagrange theorem https://ijgt.ui.ac.ir/article_29647_f443215bd6fc4ce8ef015ffd559b10cd.pdf