Advanced search
Start date
Betweenand
Related content
(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

ON TORSION-FREE NILPOTENT LOOPS

Full text
Author(s):
Mostovoy, Jacob [1] ; Perez-Izquierdo, Jose M. [2] ; Shestakov, Ivan P. [3]
Total Authors: 3
Affiliation:
[1] CINVESTAV, Dept Matemat, Apartado Postal 14-740, Mexico City 07000, DF - Mexico
[2] Univ La Rioja, Dept Matemat & Comp, Edificio CCT, C Madre Dios 53, Logrono 26006, La Rioja - Spain
[3] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05311970 Sao Paulo, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: QUARTERLY JOURNAL OF MATHEMATICS; v. 70, n. 3, p. 1091-1104, SEP 2019.
Web of Science Citations: 0
Abstract

We show that a torsion-free nilpotent loop (that is, a loop nilpotent with respect to the dimension filtration) has a torsion-free nilpotent left multiplication group of, at most, the same class. We also prove that a free loop is residually torsion-free nilpotent and that the same holds for any free commutative loop. Although this last result is much stronger than the usual residual nilpotence of the free loop proved by Higman, it is established, essentially, by the same method. (AU)

FAPESP's process: 14/09310-5 - Algebraic structures and their representations
Grantee:Vyacheslav Futorny
Support Opportunities: Research Projects - Thematic Grants