Groups and noncommutative algebra: interactions and applications
On the unit group of Z-orders in finite dimensional algebras
Bone remodeling and biomechanical analysis of maxillary alveolar bone in rats with...
| Full text | |
| Author(s): |
Goncalves, Jairo Z.
;
Souza, Gabriel A. L.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. N/A, p. 16-pg., 2024-11-25. |
| Abstract | |
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) | |
| FAPESP's process: | 20/16594-0 - Non commutative rings and applications |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Projects - Thematic Grants |