Free groups in normal subgroups of the multiplicative group of a division ring

Autor(es)

Goncalves, Jairo Z. ^[1] ; Passman, Donald S. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Math, BR-05508090 Sao Paulo - Brazil

^[2] Univ Wisconsin, Dept Math, Madison, WI 53706 - USA

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 440, p. 128-144, OCT 15 2015.
• Citações Web of Science: 6

Resumo

Let D be a division ring with center Z and multiplicative group D \textbackslash{} [0] = D-center dot, and let N be a normal subgroup of D-center dot. We investigate various conditions under which N must contain a free noncyclic subgroup. In one instance, assuming that the transcendence degree of Z over its prime field is infinite, and that N contains a nonabelian solvable subgroup, we use a construction method due to Chiba to exhibit free generators of the free subgroup. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 09/52665-0 - Grupos, anéis e álgebras: interações e aplicações
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Temático