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

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