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Bicyclic units, Bass cyclic units and free groups
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Jairo Z Gonçalves
and
Ángel del Río
Published/Copyright:
March 11, 2008
Abstract
Let G be a finite group and ℤG its integral group ring. We show that if α is a nontrivial bicyclic unit of ℤG, then there are bicyclic units β and γ of different types, such that 〈α, β〉 and 〈α, γ〉 are non-abelian free groups. In the case when G is non-abelian of order coprime to 6 we prove the existence of a bicyclic unit u and a Bass cyclic unit v in ℤG, such that 〈um, v〉 is a free non-abelian group for all sufficiently large positive integers m.
Received: 2006-11-28
Revised: 2007-06-12
Published Online: 2008-03-11
Published in Print: 2008-03-01
© Walter de Gruyter
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Articles in the same Issue
- A sectional characterization of the Dade group
- Transitive decompositions of graph products: rank 3 grid type
- Subgroups of finitary permutation groups
- Automorphisms of the standard Borel subgroup of the symplectic group over a commutative ring
- Bicyclic units, Bass cyclic units and free groups
- A presentation for Aut(Fn)
- The growth series for Higman 3
Articles in the same Issue
- A sectional characterization of the Dade group
- Transitive decompositions of graph products: rank 3 grid type
- Subgroups of finitary permutation groups
- Automorphisms of the standard Borel subgroup of the symplectic group over a commutative ring
- Bicyclic units, Bass cyclic units and free groups
- A presentation for Aut(Fn)
- The growth series for Higman 3
