One-Overlapped Factorizations of Non-abelian Groups
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One-overlapped factorizations of finite groups were introduced by Shinohara (Linear Algebra Appl. 436(4):850–857, 2012) for constructing a new class of thin Lehman matrices. However, all known examples and constructions arise from cyclic or dihedral groups. In this paper, we prove the existence of one-overlapped factorizations of non-abelian groups that are not dihedral and describe a simple construction. The corresponding incidence structures and Lehman matrices are also considered.
KeywordsDihedral group General linear group Set cover problem Thin Lehman matrix
Mathematics Subject Classification05B20 20D99
This work was supported by the Alexander von Humboldt Foundation with funds from the German Federal Ministry of Education and Research (BMBF). The author would like to thank Dr. Marco A. Pellegrini for his comments on the previous version of this paper.
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