A Note on Quasi-Periodic Factorizations

A question was raised in [3] concerning a hereditary property for quasi-periodic factorizations. In this note a result is proved which leads to a negative answer to this question.

[1]  Alexei G. Myasnikov,et al.  On Positive Theories of Groups with Regular Free Length Functions , 2007, Int. J. Algebra Comput..

[2]  A. D. Sands.  On a conjecture of G. Hajós , 1974, Glasgow Mathematical Journal.

[3]  A. D. Sands.  Factoring finite abelian groups , 2004 .