Groups in which every Lagrange subset is a factor

نویسندگان
Hooshmand, Mohammad Hadi ID 1
Kohl, Stefan ID 2

1 Department of Mathematics, Shi.C., Islamic Azad University, Shiraz, Iran

2 Fridtjof-Nansen-Strasse 3, Rostock, Germany

doi
10.22108/ijgt.2025.144957.1957
چکیده

We determine the finite groups $G$ in which every subset $A \subseteq G$ of cardinality dividing the order of $G$ is a factor, i.e. has a complement $B \subseteq G$ of cardinality $|G|/|A|$ such that $G = A \cdot B$ or $G = B \cdot A$.

کلیدواژه‌ها
Finite group, group factorization into subsets, converse of Lagrange theorem