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CONTINUITY OF $\pi$-PERFECTION FOR COMPACT LIE GROUPS

Published online by Cambridge University Press:  08 February 2005

HALVARD FAUSK  and
BOB OLIVER
HALVARD FAUSK
Affiliation:
Department of Mathematics, University of Oslo, [email protected]
BOB OLIVER
Affiliation:
LAGA, Institut Galilée, Av. J-B Clément, 93430 Villetaneuse, [email protected]
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Abstract

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.

Keywords

55P91 (primary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 1 , January 2005 , pp. 135 - 140
Copyright
© The London Mathematical Society 2005

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