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Semigroup identities on units of integral group rings

Published online by Cambridge University Press:  18 May 2009

Michael A. Dokuchaev  and
Jairo Z. Gonçalves
Michael A. Dokuchaev
Affiliation:
Instituto de Matemática e Estatistica, Universidade de Sāo Paulo, CP 66281-AG Cid. de Sāo Paulo, CEP 05389-970 Sāo Paulo-Brazil, dokucha@ime.usp.br, jzg@ime.usp.br
Jairo Z. Gonçalves
Affiliation:
Instituto de Matemática e Estatistica, Universidade de Sāo Paulo, CP 66281-AG Cid. de Sāo Paulo, CEP 05389-970 Sāo Paulo-Brazil, dokucha@ime.usp.br, jzg@ime.usp.br
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Abstract

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Let U(RG) be the group of units of a group ring RG over a commutative ring R with 1. We say that a group is an SIT-group if it is an extension of a group which satisfies a semigroup identity by a torsion group. It is a consequence of the main result that if G is torsion and R = Z, then U(RG) is an SIT-group if and only if G is either abelian or a Hamiltonian 2-group. If R is a local ring of characteristic 0 only the first alternative can occur.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 1 , January 1997 , pp. 1 - 6
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

1.Bovdi, A. A., The multiplicative group of an integral group ring (Russian) (Uzhgorod, 1987).Google Scholar
2.Gonçalves, J. Z., Integral group rings whose group of units is solvable: an elementary proof, Bol. Soc. Brasil. Mat. 16, 2 (1985), 1–9.CrossRefGoogle Scholar
3.Gongalves, J. Z. and Mandel, A., Semigroup identities on units of group algebras, Archiv. Mater. (Basel) 57 (1991), 539–545.CrossRefGoogle Scholar
4.Hartley, B. and Pickel, P. F., Free subgroups in the unit groups of integral group rings, Canad. J. Math. 32 (1980), 1342–1352.CrossRefGoogle Scholar
5.Huppert, B. and Blackburn, N., Finite groups II (Springer-Verlag, Berlin-Heidelberg, 1982).Google Scholar
6.Karpilovsky, G., Unit groups of classical rings (Oxford University Press, 1988).Google Scholar
7.Passman, D. S., The algebraic structure of group rings (Wiley-Interscience, New York, 1977).Google Scholar
8.Rosenblatt, J. M., Invariant measures and growth conditions. Trans. A.M.S. 193 (1974), 33–52.CrossRefGoogle Scholar
9.Sehgal, S. K., Topics in group rings (Marcel Dekker, New York, 1978).Google Scholar
10.Sehgal, S. K., Units in integral group rings (Wiley, New York, 1993).Google Scholar
11.Tits, J., Free subgroups in linear groups, J. Algebra 20 (1972), 250–270.CrossRefGoogle Scholar