Geodesic
Free Subgroups and the Residual Nilpotence of the Group of Units of Modular and p-Adic Group Rings
Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 321-328

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a group, let RG be the group ring of the group G over the unital commutative ring R and let U(RG) be its group of units. Conditions which imply that U(RG) contains no free noncyclic group are studied, when R is a field of characteristic p ≠ 0, not algebraic over its prime field, and G is a solvable-by-finite group without p-elements. We also consider the case R = Zp, the ring of p-adic integers and G torsionby- nilpotent torsion free group. Finally, the residual nilpotence of U(ZpG) is investigated.
DOI : 10.4153/CMB-1986-049-x
Mots-clés : 16A26, 16A40, 20CO5, group rings, group of units, free groups, residual nilpotence 
Gonçalves, Jairo Zacarias. Free Subgroups and the Residual Nilpotence of the Group of Units of Modular and p-Adic Group Rings. Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 321-328. doi: 10.4153/CMB-1986-049-x
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[1] 1. Gonçalves, J. Z., Group rings with solvable unit groups. Comm. in Algebra, 14, 1 (1986), pp. 1—20. Google Scholar

[2] 2. Gonçalves, J. Z., Free subgroups of units in group rings. Bull Can. Math. Soc. 27, 3 (1984), pp. 309–312. Google Scholar

[3] 3. Gonçalves, J. Z., Free subgroups in the group of units of group rings II. Journal of Number Theory, 21, 2 (1985), pp. 121–127. Google Scholar

[4] 4. Gonçalves, J. Z., Free groups in subnormal subgroups and the residual nilpotence of the group of units of group rings. Bull Can. Math. Soc. 27, 3 (1984), pp. 365–370. Google Scholar

[5] 5. Hartley, B. and Pickel, P. F., Free subgroups in the unit groups of integral group rings. Can. J. of Math. 32, 6(1980), pp. 1342–1352. Google Scholar

[6] 6. Musson, I., and Weiss, A., Integral group rings with residually nilpotent unit groups. Arch. Math. 38 (1982), pp. 514–530. Google Scholar

[7] 7. Sehgal, S. K., Topics in group rings. Marcel Dekker, New York, 1978. Google Scholar

[8] 8. Sehgal, S. K. and Zassenhaus, H.J., Isomorphism of integral group rings of abelian-by-nilpotent class two groups. Pre-print. Google Scholar

[9] 9. Tits, J., Free subgroups in linear groups. J of Algebra 20 (1972), pp. 250—270. Google Scholar

[10] 10. Warhurst, D. S., Topics in group rings. Thesis. University of Manchester, 1981. Google Scholar

[11] 11. Wehrfritz, B. A. F., Infinite linear groups. Springer Verlag, Berlin, 1973. Google Scholar

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