On the Burnside ring of a compact group

Gordon, Robin A.

doi:10.1090/S0002-9939-1978-0461537-0

On the Burnside ring of a compact group
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by Robin A. Gordon PDF

Proc. Amer. Math. Soc. 68 (1978), 101-107 Request permission

Abstract:

The Burnside ring $A(G)$ of an arbitrary compact group G is defined in analogy to tom Dieck’s definition for a compact Lie group. A topology is introduced on the set of conjugacy classes of closed subgroups, and a theorem of Dress on the topology of the prime spectrum of $A(G)$ for profinite G is improved and extended to this general setting.

References

General topology

Glen E. Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics, Vol. 46, Academic Press, New York-London, 1972. MR 0413144
Tammo tom Dieck, The Burnside ring of a compact Lie group. I, Math. Ann. 215 (1975), 235–250. MR 394711, DOI 10.1007/BF01343892
Andreas W. M. Dress, Notes on the theory of representations of finite groups. Part I: The Burnside ring of a finite group and some AGN-applications, Universität Bielefeld, Fakultät für Mathematik, Bielefeld, 1971. With the aid of lecture notes, taken by Manfred Küchler. MR 0360771

Contributions to the theory of the Burnside ring

Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182. MR 42109, DOI 10.1090/S0002-9947-1951-0042109-4
Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104