Elements generating a free subgroup of rank three in the multiplicative group of a division ring

Autor(es)

Goncalves, Jairo Z. ; Souza, Gabriel A. L.

• 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