Groups in which every Lagrange subset is a factor

Hooshmand, Mohammad Hadi; Kohl, Stefan

doi:10.22108/ijgt.2025.144957.1957

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	Groups in which every Lagrange subset is a factor
International Journal of Group Theory
دوره 15، شماره 1، خرداد 2026، صفحه 43-48 اصل مقاله (398.46 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2025.144957.1957
نویسندگان
Mohammad Hadi Hooshmand¹؛ Stefan Kohl^* ²
¹Department of Mathematics, Shi.C., Islamic Azad University, Shiraz, Iran
²Fridtjof-Nansen-Strasse 3, Rostock, Germany
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

مراجع
[1] R. R. Bildanov, V. A. Goryachenko and A. V. Vasilev, Factoring nonabelian finite groups into two subsets, Sib. ` Elektron. Mat. Izv., 17 (2020) 683–689. [2] M. H. Hooshmand,Basic results on an unsolved problem about factorization of finite groups, Comm. Algebra, 49 no. 7 (2021) 2927–2933. [3] M. H. Hooshmand, Some generalizations of Lagrange theorem and factor subsets for semigroups, J. Math. Ext., 11 no. 3 (2017) 77–86. [4] https://mathoverflow.net/questions/155986/factor-subsets-of-a-finite-group [5] E. I. Khukhro and V. D. Mazurov, Unsolved problems in group theory: The Kourovka Notebook, no. 19 (resp. no. 20), Sobolev Institute of Mathematics, 2018 (resp. 2022).
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Groups in which every Lagrange subset is a factor