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A class of ideals of the centre of a group ring

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Michael F. O'Reilly
Michael F. O'Reilly
Affiliation:
Department of Mathematics, Rhodes University, Grahamstown, 6140, South Africa
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Abstract

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Reynolds (1972), using character-theory, showed that the p-section sums span an ideal of the centre Z(kG) of the group algebra of a finite group G over a field k of characteristic dividing the order of G. In O'Reilly (1973) a character-free proof was given. Here we extend these techniques to show the existence of a wider class of ideals of Z(kG).

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules 20C20: Modular representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 2 , August 1981 , pp. 146 - 151
Copyright
Copyright © Australian Mathematical Society 1982

References

Broué, M. (1978) ‘Radicals, hauteurs, p-sections et blocs’, Ann. of Math. 107, 89–107.CrossRefGoogle Scholar
lizuka, K., Ito, Y., Watanabe, A. (1973), ‘A remark on the representations of finite groups IV’, Memoirs of the Faculty of General Education, Kumamato Univ., Natural Science Series, 8, 1–5.Google Scholar
O'Reilly, M. F. (1973) ‘Ideals in the centre of a group ring’, Proc. Second Internat. Conf. Theory of Groups, pp. 536–540 (Lecture Notes in Mathematics 372, Springer Verlag, Berlin).Google Scholar
Reynolds, W. F. (1972) ‘Sections and ideals of centers of group algebras’, Algebra 20, 176–181.Google Scholar