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

Katedra Matematyki (RMS/RMS1)

Wyniki badań: Wkład do czasopisma › Artykuł › recenzja

Abstrakt

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.

Język oryginału	angielski
Strony (od–do)	19-34
Liczba stron	16
Czasopismo	Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Tom	136
Identyfikatory DOI	https://doi.org/10.4171/RSMUP/136-3
Status publikacji	Opublikowano - 2016

Obszary tematyczne ASJC Scopus

Analiza
Algebra i teoria liczb
Fizyka matematyczna
Geometria i topologia

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10.4171/RSMUP/136-3

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Cytowanie

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N2 - 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.

AB - 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.

KW - Abelian groups

KW - Commutation of elements

KW - Group laws

UR - https://www.scopus.com/pages/publications/85007578579

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DO - 10.4171/RSMUP/136-3

M3 - Article

AN - SCOPUS:85007578579

SN - 0041-8994

VL - 136

SP - 19

EP - 34

JO - Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

JF - Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

ER -

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

Abstrakt

Obszary tematyczne ASJC Scopus

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