Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584121 | Journal of Algebra | 2015 | 17 Pages |
Abstract
Let D be a division ring with center Z and multiplicative group D∖{0}=D•D∖{0}=D•, and let N be a normal subgroup of D•D•. 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jairo Z. Gonçalves, Donald S. Passman,