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Free Subgroups and the Residual Nilpotence of the Group of Units of Modular and p-Adic Group Rings

Published online by Cambridge University Press:  20 November 2018

Jairo Zacarias Gonçalves
Jairo Zacarias Gonçalves*
Affiliation:
Universidade de Sāo Paulo, Instituto de Mat. E EstatísticaAG. Iguatemi, CX. Postal 20570 01000 Sāo Paulo, SP., Brazil
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Abstract

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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.

Keywords

16A2616A4020CO5group ringsgroup of unitsfree groupsresidual nilpotence
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 3 , 01 September 1986 , pp. 321 - 328
Copyright
Copyright © Canadian Mathematical Society 1986

References

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