N.D. Gupta has proved that groups which satisfy the laws for are abelian. Every law can be written in the form where belong to a free group of rank two, and the normal closure of coincides with . In this work we investigate laws of this form. In particular, we discuss certain classes of laws and show that the metabelian groups which satisfy them are abelian.
Cite this article
Witold Tomaszewski, On laws of the form equivalent to the abelian law. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 19–34DOI 10.4171/RSMUP/136-3