"Classifying spaces and a subgroup of the exceptional Lie group G_2"
Kenshi Ishiguro
Mathematics subject classification: 55R35
Abstract: We consider a problem on the conditions of a compact Lie group that
its loop space of the p-completed classifying space be a p-compact group,
as well as some related problems. A previously obtained necessary condition
is shown to be not sufficient. Our counterexample
is given by a quotient group \Gamma_2 of a subgroup of the exceptional Lie group G_2
at p=3. The 3-adic K-theory of B\Gamma_2 and BG_2 are isomorphic , though
the loop space of the 3-completion of B\Gamma_2 is not a 3-compact group.