| Texto completo | |
| Autor(es): |
Goncalves, Jairo Z.
;
Souza, Gabriel A. L.
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. N/A, p. 16-pg., 2024-11-25. |
| Resumo | |
Let FG be the group algebra of a residually torsion free nilpotent group G over a field F of characteristic 0. If (x,y) is any pair of noncommuting elements of G, we show that for any rational number r with r not equal 0, +/- 1, the subgroup < 1 + rx, 1 + ry, 1 + rxy > is free of rank 3 in the Malcev-Neumann field of fractions of FG. This result comes from a method of producing free groups of rank three in rational quaternions. In general, if a division ring D has dimension d(2) over its center Z, and if the transcendence degree of Z over its prime field F-p is >= d(2) + 3, we present a method to construct free subgroups of rank three. (AU) | |
| Processo FAPESP: | 20/16594-0 - Anéis não comutativos e aplicações |
| Beneficiário: | Francisco Cesar Polcino Milies |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |