On laws of the form abba equivalent to the abelian law
Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 19-34.

N.D. Gupta has proved that groups which satisfy the laws [x,y][x, n y] for n=2,3 are abelian. Every law [x,y][x, n y] can be written in the form abba where a,b belong to a free group F 2 of rank two, and the normal closure of a,b coincides with F 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.

DOI : 10.4171/RSMUP/136-3
Classification : 20
Mots clés : Group laws, abelian groups, commutation of elements
Tomaszewski, Witold 1

1 Silesian University of Technology, GLIWICE, POLAND
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     title = {On laws of the form $ab\equiv ba$ equivalent to the abelian law},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {19--34},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {136},
     year = {2016},
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     url = {http://www.numdam.org/articles/10.4171/RSMUP/136-3/}
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Tomaszewski, Witold. On laws of the form $ab\equiv ba$ equivalent to the abelian law. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 19-34. doi : 10.4171/RSMUP/136-3. http://www.numdam.org/articles/10.4171/RSMUP/136-3/

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