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.
Classification :
20
Mots-clés : Group laws, abelian groups, commutation of elements
Mots-clés : Group laws, abelian groups, commutation of elements
Affiliations des auteurs :
Tomaszewski, Witold 1
@article{RSMUP_2016__136__19_0, author = {Tomaszewski, Witold}, 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}, doi = {10.4171/RSMUP/136-3}, url = {http://www.numdam.org/articles/10.4171/RSMUP/136-3/} }
TY - JOUR AU - Tomaszewski, Witold TI - On laws of the form $ab\equiv ba$ equivalent to the abelian law JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2016 SP - 19 EP - 34 VL - 136 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/136-3/ DO - 10.4171/RSMUP/136-3 ID - RSMUP_2016__136__19_0 ER -
%0 Journal Article %A Tomaszewski, Witold %T On laws of the form $ab\equiv ba$ equivalent to the abelian law %J Rendiconti del Seminario Matematico della Università di Padova %D 2016 %P 19-34 %V 136 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/136-3/ %R 10.4171/RSMUP/136-3 %F RSMUP_2016__136__19_0
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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