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

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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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     title = {Free {Subgroups} and the {Residual} {Nilpotence} of the {Group} of {Units} of {Modular} and {p-Adic} {Group} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {321--328},
     year = {1986},
     volume = {29},
     number = {3},
     doi = {10.4153/CMB-1986-049-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-049-x/}
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