N-determined p-compact groups. (English summary) Fund. Math. 173 (2002), no. 3, 201–300. This paper forms part of a classification program for p-compact groups. We recall briefly that a p-compact group X is a homotopy theorist’s Lie group: it is a connected pointed p-complete space BX with the property that its loop space X has finite mod p homology. Any compact Lie group G such that π0G is a p-group determines a p-compact group by p-completing its classifying space. W. G. Dwyer and C. W. Wilkerson, Jr. [Ann. of Math. (2) 139 (1994), no. 2, 395–442; MR1274096 (95e:55019)] showed that this definition was sufficient to recover essential features of the theory of Lie groups, by establishing that any p-compact group has a “maximal torus” T, unique up to “conjugacy”, and an associated “Weyl group ” W, which is well defined up to conjugacy as a p-adic pseudo-reflection group. Subsequent work by them, D. Notbohm, the author, and others established many other Lie-like features of this theory. For surveys of this subject se
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