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On the units of a modular group ring II

Published online by Cambridge University Press:  17 April 2009

K.R. Pearson
K.R. Pearson
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria.
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Abstract

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Let R be a ring of nonzero characteristic and let G be a finite group with subgroup H. It is shown that H is a normal subgroup of the group of units of the group ring RG if and only if H is contained in the centre of G or R is the field with 2 elements, G is the symmetric group on 3 letters and H is normal in G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 3 , June 1973 , pp. 435 - 442
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Artin, E., Geometric algebra (Interscience, New York, London, 1957).Google Scholar
[2]Eldridge, Klaus E., “On normal subgroups in modular group algebras”, (unpublished).Google Scholar
[3]Lambek, J., Lectures an rings and modules (Blaisdell, Waltham, Massachusetts, 1966).Google Scholar
[4]Pearson, K.R., “On the units of a modular group ring”, Bull. Austral. Math. Soc. 7 (1972), 169–182.CrossRefGoogle Scholar