Free Subgroups in the Units of ℤ[K₈ × C_p]

Abstract

Marciniak and Sehgal (Marciniak, Z., Sehgal, S. K. (1997). Constructing free subgroups of integral group rings units. Proc. Amer. Math. Soc.125(4):1005–1009) constructed free subgroups in U(ℤ[G]) whenever Ghas a non normal finite subgroup. In this paper we construct free subgroups in U(ℤ[G]), where Gis a group whose subgroups are all normal.

Key Words:

• Integral group rings
• Free groups
• Bass cyclic units
• Hamiltonian groups

Acknowledgments

This paper is based on a chapter of my Ph.D. thesis. I thank my advisor Prof. Jairo Zacarias Gonçalves for his support and attention. I wish to thank also Prof. Vitor O. Ferreira and Prof. César Polcino Milies for their careful readings and useful comments.

Research supported by FAPESP, processo 97/13624-8.