JournalsrsmupVol. 136pp. 19–34

On laws of the form abbaab\equiv ba equivalent to the abelian law

  • Witold Tomaszewski

    Silesian University of Technology, Gliwice, Poland
On laws of the form $ab\equiv ba$ equivalent to the abelian law cover
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Abstract

N.D. Gupta has proved that groups which satisfy the laws [x,y][x,ny][x,y]\equiv [x,_ny] for n=2,3n=2,3 are abelian. Every law [x,y][x,ny][x,y]\equiv [x,_ny] can be written in the form abbaab\equiv ba where a,ba,b belong to a free group F2F_2 of rank two, and the normal closure of a,b\langle a,b \rangle coincides with F2F_2. 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 abbaab\equiv ba equivalent to the abelian law. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 19–34

DOI 10.4171/RSMUP/136-3