Sciweavers

Share
IJAC
2011

Bass Cyclic Units as Factors in a Free Group in Integral Group Ring Units

8 years 2 months ago
Bass Cyclic Units as Factors in a Free Group in Integral Group Ring Units
Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the centre. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the centre of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.
Jairo Z. Gonçalves, Ángel del R&iacu
Added 29 Aug 2011
Updated 29 Aug 2011
Type Journal
Year 2011
Where IJAC
Authors Jairo Z. Gonçalves, Ángel del Río
Comments (0)
books