On laws of the form ab ≡ ba equivalent to the abelian law

Witold Tomaszewski

doi:10.4171/RSMUP/136-3

On laws of the form ab ≡ ba equivalent to the abelian law

Witold Tomaszewski

Department of Mathematics (RMS/RMS1)

Research output: Contribution to journal › Article › peer-review

Abstract

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 ab = ba where a, b belong to a free group F₂of rank two. and the normal closure of 〈a,b〉 coincides with F₂-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.

Original language	English
Pages (from-to)	19-34
Number of pages	16
Journal	Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Volume	136
DOIs	https://doi.org/10.4171/RSMUP/136-3
Publication status	Published - 2016

Keywords

Abelian groups
Commutation of elements
Group laws

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics
Geometry and Topology

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10.4171/RSMUP/136-3

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KW - Group laws

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ER -

On laws of the form ab ≡ ba equivalent to the abelian law

Abstract

Keywords

ASJC Scopus subject areas

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