We describe K(BS 4 ) and make a connection of the order of the bundle induced from the standart representation over the four dimensional skeleton of BS 4 with the stable homotopy group π s 3 = Z 24 explaining the reasons of this connection by pulling this bundle over lens spaces.
We describe the K -ring of the classifying space of the generalized quaternion group in terms of generators and the minimal set of relations. We also compute the order of the main generator in the truncated rings.
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