Nonquasi-Periodic Factorizations for Certain Finite Abelian Groups

Hajos [2] asked if each factorization of a finite abelian group is quasi-periodic. Sands [5] exhibited a counter-example. We will show that a sizeable family of finite abelian groups admits nonquasi-periodic factorizations. We also describe a small family whose members have only quasi-periodic factorizations.