Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-07-05T13:29:23.886Z Has data issue: false hasContentIssue false

Burnside rings of finite representation type

Published online by Cambridge University Press:  17 April 2009

Alberto Raggi-Cárdenas
Affiliation:
Instituto de Matemáticas, UNAM Circuito Exterior, Ciudad Universitaria México, 04510, D.F., Mexico
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a finite group. It is proved that the localised Buinside ring Ωp(G) is of finite representation type if and only if for each p–perfect subgroup H of G, , where means the conjugacy class of K.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Curtis, C.W. and Reiner, I., Methods of representation theory I (J. Wiley, New York, 1981).Google Scholar
[2]Curtis, C.W. and Reiner, I., Methods of representation theory II (J. Wiley, New York, 1987).Google Scholar
[3]Dieck, T. tom, ‘Transformation groups and representation theory’, in Lecture Notes in Mathematics 766 (Springer-Verlag, Berlin, 1979).Google Scholar
[4]Drozd, Y. and Roiter, A., ‘Commutative rings with a finite number of indecomposable integral representations’, Math. USSR Izv I (1967), 757772.CrossRefGoogle Scholar
[5]Kratzer, C. and Thévenaz, J., ‘Fonction de Möbius d'un groupe fini et anneau de Burnside’, Comment. Math. Helv. 59 (1984), 425–38.CrossRefGoogle Scholar
[5]Yoshida, T., ‘Idempotents of Burnside rings and dress induction theorem’, J. Algebra 80 (1983), 90105.CrossRefGoogle Scholar