One-Overlapped Factorizations of Non-abelian Groups
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.