ON TORSION-FREE NILPOTENT LOOPS

Autor(es)

Mostovoy, Jacob ^[1] ; Perez-Izquierdo, Jose M. ^[2] ; Shestakov, Ivan P. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: QUARTERLY JOURNAL OF MATHEMATICS; v. 70, n. 3, p. 1091-1104, SEP 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático