Free Subgroups and the Residual Nilpotence of the Group of Units of Modular and p-Adic Group Rings
1986 ◽
Vol 29
(3)
◽
pp. 321-328
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Keyword(s):
AbstractLet 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.
1980 ◽
Vol 32
(3)
◽
pp. 596-602
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Keyword(s):
1976 ◽
Vol 28
(5)
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pp. 954-960
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Keyword(s):
2013 ◽
Vol 12
(06)
◽
pp. 1350004
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Keyword(s):
1993 ◽
Vol 35
(3)
◽
pp. 367-379
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Keyword(s):
1985 ◽
Vol 21
(2)
◽
pp. 121-127
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1997 ◽
Vol 122
(1)
◽
pp. 55-71
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Keyword(s):
1980 ◽
Vol 21
(1)
◽
pp. 151-163
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Keyword(s):
1973 ◽
Vol 25
(2)
◽
pp. 366-369
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Keyword(s):