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A note on central idempotents in group rings II

Published online by Cambridge University Press:  20 January 2009

Sônia P. Coelho
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 20.570—Ag. Iguatemi, 01000—São Paulo—Brazil
C. Polcino Milies
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 20.570—Ag. Iguatemi, 01000—São Paulo—Brazil
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Let G be a group and K a field. We shall denote by U(KG) the group of units of the group ring of G over K. Also, if X is a group, T(X) will denote the torsion subset of X, i.e., the set of all elements of finite order in X.

Group theoretical properties of U(KG) have been studied intensively in recent years and it has been found that some conditions about U(KG) imply that T = T(G) must be a subgroup of G and that every idempotent of KT must be central in KG.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

1.Coelho, S. P., A note on central idempotents in group rings, Proc. Edinburgh Math. Soc., to appear.Google Scholar
2.Hall, M., The Theory of Groups (Macmillan, New York, 1959).Google Scholar
3.Isaacs, I. M., Character Theory of Finite Groups (Academic Press, New York, 1976).Google Scholar
4.Sehgal, S. K., Topics in Group Rings (Marcel Dekker, New York, 1979).Google Scholar
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