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Bulletin of the London Mathematical Society 2005 37(1):135-140; doi:10.1112/S0024609304003601
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© London Mathematical Society

Continuity of {pi}-Perfection for Compact Lie Groups

Halvard Fausk and Bob Oliver

Department of Mathematics, University of Oslo Norway; fausk{at}math.uio.no
LAGA, Institut Galilée Av. J-B Clément, 93430 Villetaneuse, France; bobol{at}math.univ-paris13.fr

Received 13 May 2003. Revision received 18 November 2003.

Let G be a compact Lie group, and let {pi} be any prime or set of primes. A ‘{pi}-perfection map’ is constructed: that is, a continuous function from the space of conjugacy classes of all closed subgroups of G to the space of conjugacy classes of {pi}-perfect subgroups with finite index in their normalizer. This is used to show that the idempotent elements of the Burnside ring of G localized at {pi} are in bijective correspondence with the open and closed subsets of the space of conjugacy classes of {pi}-perfect subgroups of G with finite index in their normalizer. 2000 Mathematics Subject Classification 55P91 (primary).

The second author was partially supported by UMR 7539 of the CNRS.


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