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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Constructing free groups in a normal subgroup of the multiplicative group of division rings

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Author(s):
Goncalves, Jairo Z.
Total Authors: 1
Document type: Journal article
Source: Journal of Group Theory; v. 18, n. 5, p. 829-843, SEP 2015.
Web of Science Citations: 2
Abstract

Let D be a division ring with center k and multiplicative group D-dagger, and let N be a normal subgroup of D-dagger. Assuming that N contains a subgroup G which is nonabelian torsion-free polycyclic-by-finite (not abelian-by-finite), we construct a free noncyclic subgroup of N in terms of elements of G. We also show that if char k not equal 2, D is generated over k by the torsion-free polycyclic-by finite group G (not abelian-by-finite), and if it is possible to extend the involution x({*}) = x(-1) of G to a k involution of D, then D Z contains a free symmetric pair. (AU)

FAPESP's process: 09/52665-0 - Groups, rings and algebras: interactions and applications
Grantee:Francisco Cesar Polcino Milies
Support type: Research Projects - Thematic Grants