a1 Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia. email@example.com
a2 University of Turku, Department of Mathematics, 20014 Turku, Finland; firstname.lastname@example.org
a3 Turku Centre for Computer Science, 20014 Turku, Finland; email@example.com
In the paper we study abelian versions of the critical factorization theorem. We investigate both similarities and differences between the abelian powers and the usual powers. The results we obtained show that the constraints for abelian powers implying periodicity should be quite strong, but still natural analogies exist.
(Received November 2 2010)
(Accepted August 2 2011)
(Online publication September 22 2011)
Mathematics Subject Classification:
∗ Supported in part by the Academy of Finland under the grant 121419, by Finnish Cultural Foundation, by Russian Foundation of Basic Research (grants 10-01-00424, 09-01-00244).