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Hooshmand, Mohammad, Kohl, Stefan. (1404). Groups in which every Lagrange subset is a factor. , (), -. doi: 10.22108/ijgt.2025.144957.1957
Mohammad Hadi Hooshmand; Stefan Kohl. "Groups in which every Lagrange subset is a factor". , , , 1404, -. doi: 10.22108/ijgt.2025.144957.1957
Hooshmand, Mohammad, Kohl, Stefan. (1404). 'Groups in which every Lagrange subset is a factor', , (), pp. -. doi: 10.22108/ijgt.2025.144957.1957
Hooshmand, Mohammad, Kohl, Stefan. Groups in which every Lagrange subset is a factor. , 1404; (): -. doi: 10.22108/ijgt.2025.144957.1957

Groups in which every Lagrange subset is a factor

International Journal of Group Theory
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 تیر 1404    اصل مقاله (383.19 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2025.144957.1957
نویسندگان
Mohammad Hadi Hooshmand1؛ Stefan Kohl* 2
1Department of Mathematics Islamic Azad University, Shiraz Branch, 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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