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

Abstract

Let G be a compact Lie group, and let π be any prime or set of primes. A ‘π-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 π-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 π are in bijective correspondence with the open and closed subsets of the space of conjugacy classes of π-perfect subgroups of G with finite index in their normalizer. 2000 Mathematics Subject Classification 55P91 (primary).