PERMUTATIONS WITH A DISTINCT DIVISOR PROPERTY

A finite group of order n is said to have the distinct divisor property (DDP) if there exists a permutation g1, . . . , gn of its elements such that g −1igi+1 6= g−1j gj+1 for all 1 ≤ i < j < n. We show that an abelian group is DDP if and only if it has a unique element of order 2. We also describe a construction of DDP groups via group extensions by abelian groups and show that there exist infinitely many non abelian DDP groups