A few examples of $p$-good and $p$-bad classifying spaces

Abstract

We give examples of spaces which are good and bad at different primes in the sense of Bousfield and Kan in any arbitrary combination and investigate which impact the existence of a Sylow $p$-subgroup has on the homotopy type on the classifying space and under which conditions the homotopy type of wedges of classifying spaces is good or bad for a solid ring $R$. We give results relating to various other $R$-homological structures and a collection of examples.