Groups in which every Lagrange subset is a factor

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics Islamic Azad University, Shiraz Branch, Iran

2 Fridtjof-Nansen-Strasse 3, Rostock, Germany

10.22108/ijgt.2025.144957.1957

Abstract

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 $G = B \cdot A$.

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References

[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).
International Journal of Group Theory

Articles in Press, Corrected Proof
Available Online from 17 July 2025

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History

  • Receive Date: 18 April 2025
  • Revise Date: 23 June 2025
  • Accept Date: 05 July 2025
  • Published Online: 17 July 2025

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